8.1
Chapter 8 Mensuration
Chapter 8
Mensuration
WARM-UP EXERCISE
1. Find the unknown in each of the following figures. (Correct your answers to 3 significant
figures if necessary.)
(a)
26 cm
18 cm
(b)
(c)
x cm
z cm
30 cm
50 cm
y cm
24 cm
2. Find the volume of each of the following solids. (Express your answers in terms of  if
necessary.)
10 cm
(a)
4 cm
(b)
3 cm
6 cm
5 cm
12 cm
3 cm
(c)
8 cm
8 cm
3. Find the total surface area of each of the following solids. (Correct your answers to
3 significant figures if necessary.)
(a)
(b)
6 cm
20 cm
(c)
35 cm
8 cm
10 cm
18 cm
12 cm
4. If x : y : z  1 : 4 : 6,
(a) (i) express y in terms of x.
(ii) express z in terms of x.
(b) find x : x  y : x  y  z.
5. (a) Given that y  3x, if x increases by 5%, find the percentage increase in y.
(b) Given that y  5x 3, if x decreases by 20%, find the percentage decrease in y.
8.2
New Trend Mathematics S3B — Junior Form Supplementary Exercises
6. In each of the following figures, ABC  ADE. Find the unknowns.
A
(a)
(b)
4 cm
2 cm
E
D
D
y cm
B
C
x cm
A
8 cm
4 cm
B
(c)
A
6 cm
z cm
D
E
8 cm
E
5 cm
9 cm
C
B
10 cm
C
BUILD-UP EXERCISE
[ This part provides two extra sets of questions for each exercise in the textbook, namely Elementary Set and
Advanced Set. You may choose to complete any ONE set according to your need. ]
Exercise 8A
[ In this exercise, unless otherwise stated, correct your answers to 3 significant figures if
necessary. ]
 Elementary Set
Level 1

1. Complete the following table.
Shape of the base of a pyramid
Height
2 cm
(a)
4 cm
2 cm
Ex.8A Elementary Set
4 cm
(b)
5 cm
3 cm
3 cm
(c)
(d)
2 cm
5 cm
1.5 cm
6 cm
13 cm
8 cm
12 cm
6 cm
(e)
4 cm
12 cm
10 cm
Base area
Volume
8.3
Chapter 8 Mensuration
2. The base of a pyramid is an isosceles right-angled
triangle where the lengths of the two equal sides are
8 cm. The height VE of the pyramid is 15 cm. Find the
volume of the pyramid.
V
15 cm
C
8 cm
3. In the figure, VABC is a pyramid. ABC is an isosceles
right-angled
triangle.
If
AB  AC  40 cm
and
VB  VC  50 cm, find the volume of pyramid VABC.
8 cm
E
A
B
V
C
A
B
V
5. In the figure, VABCD is a right pyramid. Its base ABCD
is a square with sides of 6 cm each. E is a point on BC
such that VE  BC and VE  10 cm. Find the total surface
area of the pyramid.
10 cm
C
D
E
A
6 cm
B
Level 2
V
6. In the figure, VABCD is a right pyramid. The base ABCD
is a square with sides of 5 cm each. The slant edge is
8 cm long.
(a) Find the height VO of the pyramid.
8 cm
D
(b) Find the volume of the pyramid.
A
7. The figure shows the net of a right pyramid where the
base is a square with sides of 16 cm each.
(a) Find the total surface area of the pyramid.
(b) Find the height of the pyramid.
(c) Find the volume of the pyramid.
C
O
5 cm B
17 cm
16 cm
Ex.8A Elementary Set
4. The height and volume of a pyramid are 12 cm and 120 cm 3 respectively. Its base is a
rectangle with dimensions 6 cm  x cm. Find x.
8.4
New Trend Mathematics S3B — Junior Form Supplementary Exercises
Ex.8A Elementary Set
V
8. The figure shows a frustum with right-angled triangular
bases where AC  15 cm, AB  12 cm, PQ  12 cm and
AP  10 cm.
(a) By using similar triangles VPQ and VAC, find VA.
(b) By using similar triangles VPR and VAB, find PR.
R
Q
P
(c) Hence, find the volume of the frustum ABCQPR.
B
C
A
 Advanced Set
Level 1

1. The figure shows a right pyramid with a regular hexagonal
base. The base area and height of the pyramid are 50 cm 2
and 6 cm respectively. Find the volume of the pyramid.
6 cm
50 cm2
Ex.8A Advanced Set
2. It is given that the base of a pyramid is a triangle with base a cm and height b cm. If the
height of the pyramid is h cm, express the volume of the pyramid in terms of a, b and h.
3. In the figure, ABCD is a trapezium where AB  16 cm,
AD  10 cm and CD  20 cm.
A
16 cm
B
10 cm
(a) Find the area of trapezium ABCD.
(b) If trapezium ABCD is a base of a pyramid with a height
of 20 cm, find the volume of the pyramid.
D
20 cm
C
4. The height and volume of a pyramid are 12 cm and 100 cm 3 respectively. If the base of the
pyramid is a square, find the length of each side of the square base.
Level 2
5. The base of a right pyramid is a square with an area of 81 cm 2. The height is 15 cm. Find
the length of the slant edge of the pyramid.
8.5
Chapter 8 Mensuration
6. In the figure, VABC is a pyramid. ABC is an isosceles
right-angled triangular base where AB  AC  30 cm.
The height VA of the pyramid is 20 cm.
V
20 cm
(a) Find the area of VBC.
30 cm
C
A
(b) Find the total surface area of the pyramid.
30 cm
B
7. In the figure, VABCD is a right pyramid where the base
is a rectangle with dimensions 24 cm  10 cm. The
slant edge is 30 cm long.
(a) Find the height VE of the pyramid.
V
30 cm
B
(b) Find the volume of the pyramid.
8. In the figure, ABCDEFGH is a cuboid with the height
of 50 cm. Its base is a square with dimensions
20 cm  20 cm. VEFGH is a right pyramid with the
same height as the cuboid.
E
24 cm D
A
D
A
V
B
C
50 cm
(a) Find the total surface area of pyramid VEFGH.
E
20 cm
F
(b) If pyramid VEFGH is removed from the cuboid,
find the total surface area of the remaining solid.
G 20 cm H
9. If a solid metallic square-based pyramid is melted and
recast to form another square-based pyramid which is
21% higher than the original pyramid, find the
percentage decrease in the length of each side of the
square base.
V
10. In the figure, VABCD is a square-based right pyramid.
After removing right pyramid VPQRS from pyramid
VABCD, a frustum with square bases is formed. It is
given that AB  20 cm, PQ  12 cm and PA  8 cm.
S
P
(a) By considering similar triangles VPQ and VAB,
find VA and the height of the pyramid VABCD.
(b) Hence, find the volume of frustum.
(c) Find the height of VAB from point V.
(d) Hence, find the total surface area of frustum
PQRSDABC.
R
Q
C
D
A
B
Ex.8A Advanced Set
(c) Find the total surface area of the pyramid.
C
10 cm
8.6
New Trend Mathematics S3B — Junior Form Supplementary Exercises
Exercise 8B
[ In this exercise, unless otherwise stated, correct your answers to 3 significant figures if
necessary. ]
 Elementary Set
Level 1

1. Find the volume of each of the following right circular cones. (Express your answers in
terms of .)
(a)
(b)
(c)
24 cm
25 cm
9 cm
15 cm
10 cm
4 cm
2. Find the curved surface area of each of the following right circular cones. (Express your
answers in terms of .)
(a)
5 cm
(b)
0.9 m
(c)
Ex.8B Elementary Set
16 cm
20 cm
24 cm
4m
3. Both the diameter and slant height of a right circular cone are 24 cm.
(a) Find the total surface area of the cone in terms of .
(b) Find the volume of the cone.
4. The figure shows an inverted right conical paper cup. The
capacity of the paper cup is 180 cm 3 and the base radius is
4 cm.
(a) Find the height of the paper cup.
(b) If the cup is fully filled with water, find the area of the
wet surface.
4 cm
8.7
Chapter 8 Mensuration
5. The figure shows an inverted right conical popcorn cup
formed by rolling up a paper sector. It is given that the slant
height of the popcorn cup is 20 cm, and the perimeter of the
base is 50 cm.
(a) Find the area of the paper sector.
20 cm
(b) If the cost of paper for making the popcorn cup is
$6/m 2, find the cost of paper for making 200 popcorn
cups.
Level 2
6. 300 pieces of identical conical chocolate are made from 1 000 cm 3 of chocolate. If the
height of each piece of chocolate is 1 cm, find its base radius.
7. If a right circular cone is formed by rolling up the sector as
shown,
16 cm
(c) find the volume of the cone.
8. The spinning top shown in the figure is formed by three
parts. I and II are right cylinders. III is an inverted right
circular cone.
(a) Find the volume of the spinning top in terms of .
(b) Find the total surface area of the spinning top.
Ex.8B Elementary Set
(a) find the base radius of the cone.
(b) find the height of the cone.
22 cm
1 cm
3 cm
I
2 cm
II
3 cm
III
5 cm
9. A right circular frustum is formed by rotating trapezium
ABCD 360 about the axis AD. It is given that AB  6 cm,
AD  9 cm and DC  15 cm.
(a) Find the volume of the frustum in terms of .
(b) Find the total surface area of the frustum.
A 6 cm B
9 cm
D
15 cm
C
8.8
New Trend Mathematics S3B — Junior Form Supplementary Exercises
Ex.8B Elementary Set
10. The figure shows an inverted right conical funnel with the
base radius of 5 cm and height of 16 cm. Initially, the
funnel is fully filled with water. After a while, the water
level drops to 8 cm.
(a) Find the radius of the water surface.
5 cm
16 cm
(b) What percentage of water is dripped from the funnel?
 Advanced Set
Level 1
8 cm

1. Find the volume and total surface area of each of the following right circular cones.
(Express your answers in terms of .)
(a)
(b)
16 cm
(c)
16 cm
24 cm
25 cm
12 cm
17 cm
2. The slant height of a right circular cone is 18 cm and the height is half of the slant height.
Ex.8B Advanced Set
(a) Find the volume of the cone in terms of .
(b) Find the total surface area of the cone.
3. The figure shows a right circular conical hat formed by
rolling up a paper sector. It is given that the slant height of
the hat is 25 cm and the perimeter of the base is 18 cm.
25 cm
(a) Find the area of the paper sector in terms of .
(b) If the cost of paper for making the hat is $10/m 2, find
the cost of paper for making 50 conical hats.
Level 2
1
of the
3
metal is recast to form a right circular cone with the base same as the original cylinder.
Find the height of the cone.
4. (a) A metallic right cylinder with both base radius and height of 10 cm is melted.
(b) The remaining metal is recast to form another right circular cone with the base same as
the original cylinder. Find the total surface area of this cone.
Chapter 8 Mensuration
8.9
5. The figure shows an ice-cream cone where the volume of
the ice-cream is 400 cm 3. The height of the cone is 12 cm
and it is filled with ice-cream. The ratio of the volume of
ice-cream outside the cone to that inside the cone is 3  5,
find the radius of the ice-cream cone.
12 cm
6. The figure shows a chocolate in the shape of a right circular
frustum. The upper and lower base diameters are 2 cm and
3 cm respectively.
2 cm
(a) Find the volume of the chocolate.
1 cm
(b) It is given that every cm 3 of chocolate weighs 3 g. How
many chocolates as shown in the figure can be
produced from 1 kg of chocolate?
7. The figure shows a paper sector with an area of 120 cm 2.
If a right circular cone is formed by rolling up the paper
sector,
(a) find the base radius of the cone.
120cm 2
(b) find the height of the cone.
(c) find the volume of the cone.
8. The figure shows an inverted right conical cup containing
8 cm 3 of water. The diameter of the water surface is 4 cm
and the water surface is 2 cm below the rim of the cup.
(a) Find the depth of water.
2 cm
4 cm
(b) Find the area of the wet surface.
(c) Find the capacity of the cup.
9. Figure A shows a right circular paper cone where the base radius and height are 7 cm and
24 cm respectively. When the cone shown in figure A is cut along a slant height, a sector
shown in figure B is formed. Two such sectors are joined to form th e sector in figure C, and
then rolled up to form a right circular cone.

24 cm
2
7 cm
Figure A
Figure B
Figure C
Ex.8B Advanced Set
3 cm
8.10
New Trend Mathematics S3B — Junior Form Supplementary Exercises
(a) Find the base radius of the new cone.
(b) Find the height of the new cone.
(c) Find the volume of the new cone. Is the volume of the new cone twice that of the cone
in figure A?
Ex.8B Advanced Set
10. The figure shows a rocket model made up of three parts.
Solid I is a right circular cone. Solid II is a right cylinder.
Solid III is a right circular frustum.
8 cm
15 cm
I
15 cm
II
15 cm
III
(a) Find the volume of solid III in terms of .
(b) Find the volume of the rocket model in terms of .
(c) Find the total surface area of the rocket model.
12 cm
Exercise 8C
[ In this exercise, unless otherwise stated, express your answers in terms of  if necessary. ]
 Elementary Set
Level 1

1. Find the value of x in each of the following. (Correct your answers to 3 significant figures
if necessary.)
(a) x 3  27
(b) x 3  10
(c) x 3  
Ex.8C Elementary Set
2. The radius of a sphere is 6 cm.
(a) Find the volume of the sphere.
6 cm
(b) Find the surface area of the sphere.
3. The diameter of a sphere is 8 cm.
(a) Find the volume of the sphere.
(b) Find the surface area of the sphere.
8 cm
Chapter 8 Mensuration
8.11
4. If the base area of a hemisphere is 54 cm 2, find the
curved surface area of the hemisphere.
54cm2
5. If the volume of a sphere is 10 cm 3, find the radius of the sphere. (Correct your answer to
3 significant figures.)
6. If the volume of a sphere is
4
 cm3 , find the surface area of the sphere.
3
7. If the surface area of a sphere is 64 cm 2, find the volume of the sphere.
Level 2
(a) Find the surface area of the sphere.
(b) Find the volume of the sphere.
O
B
9. A metal hemisphere with the radius of 4 cm is melted and recast to form a metal sphere.
(a) Determine whether the total surface area of the solid is increased or decreased.
(b) Find the percentage increase / percentage decrease in the total surfac e area of the solids.
(Correct your answer to 3 significant figures.)
10. The figure shows a right cylindrical container with
water. After putting a number of metal balls with
diameters of 1 cm each into the container, the water
level rises 2 cm. Assume that all the metal balls are
fully immersed in water and water does not overflow,
find the number of metal balls put in the water.
10 cm
11. A pill with the length of 15 mm is shown in the figure.
If both ends of the pill are hemispheres,
(a) find the volume of the pill.
(b) find the total surface area of the pill.
15 mm
5 mm
Ex.8C Elementary Set
A
8. In the figure, O is the centre of the circle, the
circumference is 36 cm. A sphere is formed by
rotating the circle 360 about diameter AOB.
8.12
New Trend Mathematics S3B — Junior Form Supplementary Exercises
 Advanced Set
Level 1

1. Find the value of y in each of the following. (Correct your answers to 3 significant figures
if necessary.)
(a) y 3  64
(b) y 3  25
(c) y 3  27
2. Find the volume and total surface area of each of the following solids.
(a)
(b)
(c)
Diameter of the hemisphere
is 10 cm.
Circumference of the base of
the hemisphere is 20 cm.
Radius of the sphere
is 8 cm.
Ex.8C Advanced Set
3. If the volume of a sphere is 100 cm 3, find the diameter of the sphere. (Correct your answer
to 3 significant figures.)
4. A hemispherical pudding with the volume of 144 cm 3 is
shown in the figure. Find its total surface area.
5. If the surface area of a sphere is 3 600 cm 2, find the volume of the sphere.
Level 2
6. If the outer diameter of a hollow metal sphere is 12 mm and the thickness is 2 mm, find the
volume of metal required to form the metal sphere.
7. The figure shows a sculpture formed by two hemispheres.
The upper part is a hemisphere with the radius of 0.4 m and
the lower part is a hemisphere with the radius of 1 m.
(a) Find the volume of the sculpture.
(b) Find the total surface area of the sculpture.
Chapter 8 Mensuration
8.13
8. A few years ago, the standard diameter of a table tennis ball for competition changed from
38 mm to 40 mm. Find the percentage increase in the surface area of a table tennis ball for
competition. (Correct your answer to 3 significant figures.)
9. An inverted right pyramid is removed from a solid
hemisphere, where the square base of the pyramid has been
inscribed in the base of the hemisphere. Given that the slant
edge of the pyramid is 5 cm long, find the volume of the
remaining solid. (Correct your answer to 3 significant
figures.)
B
A
C
D
5 cm
V
(b) Now, 10 more metal balls with diameters of 2.4 cm
each are put into the container. Assume that the metal
balls are fully immersed in water and water does not
overflow, how much does the water level rise?
(Correct your answers to 3 significant figures.)
12 cm
15 cm
11. Figure A shows a hemisphere with the radius of r cm. Figure B shows a solid which is
formed by removing an inverted right circular cone from a right circular c ylinder. The base
radii and heights of the cone and cylinder are all r cm.
z cm
z cm
Figure A
Figure B
Figure C
Figure D
(a) Show that the volumes of solids in figures A and B are equal.
(b) Figures C and D show the cross-sections of figures A and B respectively, and both of
them are z cm from the bases. Show that the areas of the two cross-sections are equal.
Ex.8C Advanced Set
10. In the figure, a metal ball with the radius of 5 cm is inside a
container in the shape of right prism. The base of the
container is a rectangle with dimensions 15 cm  12 cm.
Water is poured into the container until the metal ball is just
covered by water.
(a) Find the volume of water.
8.14
New Trend Mathematics S3B — Junior Form Supplementary Exercises
Exercise 8D
[ In this exercise, unless otherwise stated, correct your answers to 3 significant figu res if
necessary. ]
 Elementary Set
Level 1

1. Which of the following formulae is the one for the area of
the regular pentagon as shown?
1
I.
25  10 5 a
4
1
II.
25  10 5 a 2
4
1
III.
25  10 5 a 3
4
a
a
2. The figure shows a right frustum with square bases. Which
of the following formulae is the one for the total surface
area of the frustum? Which one is the formula for its
volume?
I.
h
Ex.8D Elementary Set
(a 2  ab  b 2 )h
3
m
b
II. a  b  2am  2bm
2
2
3. A and B are two uniform cross-sections of two similar right
prisms.
(a) Find the ratio of the total surface area of the small
prism to that of the large prism.
(b) Find the ratio of the volume of the small prism to that
of the large prism.
3 cm
4 cm
A
B
4. The figure shows two similar solids A and B.
5 cm
2 cm
A
B
(a) Find the ratio of the total surface area of solid A to that of solid B.
(b) Find the ratio of the volume of solid A to that of solid B.
5. The ratio of the length of a model car to that of the real car is 1 : 24. If the area of the
windscreen of the real car is 1 m 2, find the area of the windscreen of the model car in cm 2.
8.15
Chapter 8 Mensuration
6. In the figure, A and B are two similar solids. If the area
of the cross-section of solid A is 84 cm 2, find the area
of the cross-section of solid B. (Express your answer in
terms of .)
8 cm
12 cm
B
A
7. In the figure, A and B are two similar solids. If the
volume of solid B is 6 cm 3, find the volume of solid A.
10 cm
4 cm
B
A
8. According to the following ratios of the volumes V 1 : V 2 of similar solids, find the ratios of
their corresponding lengths l 1 : l 2 and the ratios of their total surface areas A 1 : A 2.
(a) V 1 : V 2  125 : 512
(b) V 1 : V 2  64 : 27
9. According to the following ratios of the total surface areas A 1 : A 2 of similar solids, find the
ratios of their corresponding lengths l 1 : l 2 and the ratios of their volumes V 1 : V 2.
(a) A 1 : A 2  4 : 25
(b) A 1 : A 2  121 : 169
10. In the figure, the top of the solid is a square with sides
of 6 cm each. The volume of the solid is 792 cm 3. If a
similar solid is produced such that the area of the top is
2.25 times of the given one, find the volume of the new
solid.
11. If the radius of a spherical balloon increases by 15%, find the percentage increase in the
volume of the balloon.
12. The figure shows an inverted right conical paper cup
with water. The depth of water is 5 cm. After drinking
half of the water, what is the depth of water?
5 cm
Ex.8D Elementary Set
Level 2
8.16
New Trend Mathematics S3B — Junior Form Supplementary Exercises
 Advanced Set
Level 1

2a
1. In the following formulae, which one is the formula for the
area of the ellipse as shown?
I. (a  b)
2b
II. ab
4
III. a 2 b
3
2. Which of the following formulae is the one for the total
surface area of the regular icosahedron as shown? Which
one is the formula for its volume?
5 3a 2
5
II.
(3  5 )a 3
12
I.
a
Ex.8D Advanced Set
3. A and B are two uniform cross-sections of two similar
prisms.
(a) Find the ratio of the total surface area of the large prism
to that of the small one.
A
(b) Find the ratio of the volume of the large prism to that of
the small one.
Perimeter
 28 cm
4. A and B are two similar bowling pins.
(a) Find the ratio of the total surface area of the small
bowling pin to that of the large one.
(b) Find the ratio of the volume of the small bowling pin to
that of the large one.
B
Perimeter
 21 cm
50 cm
30 cm
A
B
1
of his real height is 600 cm 3. If a
8
similar bronze statue is produced with its height equals 1.5 times the real height of Bruce
Lee, what is its volume?
5. The volume of a figure of Bruce Lee with height
6. In the figure, A and B are two similar buckets. Given that
the capacity of bucket B is 17 L, what is the capacity of
bucket A?
36 cm
A
20 cm
B
8.17
Chapter 8 Mensuration
Level 2
7. When a metal rod is heated, the length of the rod increases by 8%. Find the percentage
increase in volume of the metal rod.
8. A and B are two similar sectors with areas 36 cm 2 and
25 cm 2 respectively. Two right circular cones are formed
by rolling up the two sectors.
(a) Find the ratio of the base radius of the large cone to that
of the small one.
B
A
(b) Find the ratio of the volume of the large cone to that of
the small one.
(b) Find the ratio of the base area of bottle A to that of
bottle B in the form of 1 : k.
A
10. Ice-cream in two different sizes served in two similar
ice-cream cones A and B are sold in a convenience store.
The selling price of a small ice-cream is $2 and that of the
big one is $4. Given that the ratio of the heights of the two
cones is 2 : 3, ice-cream in which cone is more economical?
Explain briefly.
B
A
B
11. The ratio of the radius of metal ball A to that of metal
ball B is 2 : 3. After melting the two metal balls, all the
metal is used to recast metal ball C.
(a) Find the ratio of the volume of metal ball B to that of
metal ball C.
441
(b) If the volume of metal ball B is
cm3 , find the
10
radius of metal ball C.

A
B
C
Ex.8D Advanced Set
9. A and B are two similar bottles with the capacities of
750 mL and 1 200 mL respectively.
(a) Find the ratio of the height of bottle A to that of bottle
B in the form of 1 : k.
8.18
New Trend Mathematics S3B — Junior Form Supplementary Exercises
Ex.8D Advanced Set
12. A cone is divided into 3 portions A, B and C by planes
parallel to the base. The ratio of the slant heights of
portions A, B and C is 1 : 2 : 1.
(a) Find the ratio of the curved surface areas of portions A,
B and C.
(b) Find the ratio of the volumes of portions A, B and C.
CHAPTER TEST
A
B
C
(Time allowed: 1 hour)
Section A (1) [ 3 marks each ]
1. The base of a pyramid is a right-angled triangle with sides
3 cm, 4 cm and 5 cm. If the height of the pyramid is 6 cm,
find the volume of the pyramid.
6 cm
5 cm
3 cm
4 cm
2. The figure shows a right circular cone. Find the volume of
the cone. (Express your answer in terms of .)
12 cm
14 cm
3. The figure shows a right circular cone. Find the curved
surface area of the cone. (Correct your answer to
3 significant figures.)
12 cm
4 cm
4. If the diameter of a sphere is 5 cm, find the volume of the sphere. (Express your answer in
terms of .)
5. The surface area of a sphere is equal to the total surface area of a hemisphere. If the ratio of
the radius of the sphere to that of the hemisphere is 1 : k, find the value of k. (Correct your
answer to 3 significant figures.)
6. The volumes of two cubes are 320 cm 3 and 135 cm 3. Find the ratio of the length of a side of
the large cube to that of the small one.
Chapter 8 Mensuration
8.19
Section A (2) [ 6 marks each ]
7. In the figure, VABCD is a right pyramid where
ABCD is a square with sides of 8 cm each. The
slant edge is 10 cm long. E is a point on CD
such the VE  CD. VO is the height of the
pyramid.
V
10 cm
A
(a) (i) Find the length of VE.
(ii) Find the total surface area of the
pyramid.
D
O
B
8 cm
E
C
(b) (i) Find the length of VO.
(ii) Find the volume of the pyramid.
(Correct your answers to 3 significant figures
if necessary.)
8. Figure A shows a right circular cone whose
base radius and height are 2x cm and x cm
respectively. Figure B shows a right circular
cone whose base radius and height are x cm
and 2x cm respectively.
2x cm
x cm
2x cm
Figure A
(a) Find the ratio of the volume of the cone in
figure A to that in figure B.
(b) Find the ratio of the curved surface area of
the cone in figure A to that in figure B.
x cm
Figure B
9. The figure shows an inverted right conical
paper cup with water. If Kristy drinks 27.1% of
the water,
(a) find the percentage decrease in the radius
of water surface.
(b) find the percentage decrease in the wet
surface area.
10. The figure shows a right circular cylindrical
container with water. The base diameter of the
container is 12 cm and the depth of water is
h cm. If a sphere with the radius of r cm is put
into the water, the sphere is just covered by
water.
(a) Express h in terms of r.
(b) If the radius of the sphere is 3 cm, find the
value of h.
r cm
h cm
12 cm
12 cm
8.20
New Trend Mathematics S3B — Junior Form Supplementary Exercises
Section B
11. The figure shows a glass filled with fruit juice. The inner
glass is in a shape of a right circular frustum.
(a) Find the capacity of the glass.
(4 marks)
8 cm
1 cm
6 cm
(b) If the surface of fruit juice is 1 cm below the rim of the
glass, find the volume of fruit juice in the glass.
(4 marks)
(c) A number of cherries with the volume of 3 cm 3 each are
immersed into the fruit juice. Assume that all the
cherries are covered with fruit juice, at most how many
cherries can be put into the glass before the fruit juice
overflow?
(5 marks)
(Express your answers in terms of  if necessary.)
2 cm
Multiple Choice Questions [ 3 marks each ]
12. The height of a right pyramid is 18 cm
and the base area is 1 250 cm 2. The
volume of the pyramid is
A. 22 500 cm 3.
B. 11 250 cm 3.
C. 7 500 cm 3.
D. 5 625 cm 3.
□
15. The base of a right pyramid is a square.
If the total surface area of the pyramid is
256 cm 2 and the area of one of the lateral
faces is 40 cm 2, find the length of each
side of the square base. (Correct your
answer to 1 decimal place.)
A. 6.3 cm
B. 9.8 cm
C. 12.6 cm
13. The base radius of a right circular cone is
6 cm and the volume is 96 cm 3. The
slant height of the cone is
A. 6 cm.
B. 6.6 cm. (corr. to 1 d.p.)
C. 8 cm.
D. 10 cm.
□
□
D. 14.7 cm
16. After removing right pyramid VABCD
from right pyramid VEFGH, right
frustum ABCDEFGH is formed as shown
in the figure. The upper and lower bases
of the frustum are both squares. If
AB  3 cm, EF  9 cm and VP  4 cm, find
the volume of the frustum.
14. The base diameter of a right circular
cone is 9 cm and the height is 8 cm. Find
the curved surface area of the cone.
(Correct your answer to 3 significant
figures.)
V
C
D
P
A
A. 113 cm 2
B
E
H
B. 130 cm 2
C. 170 cm 2
D. 1 020 cm 2
Q
□
F
G
Chapter 8 Mensuration
A. 156 cm 3
C. 576 cm 2.
B. 312 cm 3
D. 2 304 cm 2.
C. 360 cm 3
□
D. 936 cm 3
17. Find the total surface area of the right
circular cone as shown in the figure.
(Correct your answer to 3 significant
figures.)
8.21
□
20. The following figure shows the
cross-section of a UFO model. The
model consists of two hemispheres with
radii of 6 cm each, and a right cylinder
with the base diameter of 20 cm and
height of 1 cm. The volume of the UFO
model is
20 cm
20 cm
6 cm
16 cm
1 cm
A. 1 290 cm 2
B. 1 810 cm
6 cm
2
C. 2 090 cm 2
D. 3 380 cm 2
A. 244 cm 3.
□
B. 293 cm 3.
C. 388 cm 3.
18. In the figure, the radius of the sector is
18 cm and the arc of the sector is 24 cm.
A right circular cone is formed by rolling
up the sector, find the volume of the cone.
(Correct your answer to 3 significant
figures.)
18 cm
D. 964 cm 3.
□
21. There are two similar soft drink bottles
with the base diameters of 6 cm and 9 cm.
Given that the capacity of the small soft
drink bottle is 400 mL, find the capacity
of the large one.
24 cm
A. 2 020 cm 3
B. 2 710 cm 3
C. 4 070 cm 3
D. 6 070 cm 3
□
6 cm
9 cm
A. 600 mL
19. If the diameter of a sphere is 24 cm, the
surface area of the sphere is
2
A. 192 cm .
B. 288 cm 2.
B. 900 mL
C. 1 350 mL
D. 1 500 mL
□
8.22
New Trend Mathematics S3B — Junior Form Supplementary Exercises
22. If both the base radius and the height of a
right circular cone increase by 10%, the
percentage increase in the volume of the
cone is
?
A. 10%.
B. 21%.
C. 30%.
D. 33.1%.
□
5 cm
4
cm
25
4
B.
cm
15
C. 2 cm
32
D.
cm
15
A.
23. The figure shows an inverted right
conical paper cup with water. If more
water is poured into the cup to make
the water level increases by 100%
(assuming water does not overflow), the
percentage increase in the volume of
water is
□
26. In the figure, a pyramid is divided into
three solids by planes parallel to the base.
The heights of the three solids are h1, h2
and h3 where h1 : h2 : h3  1 : 2 : 3. Find the
ratio of the volumes of the three solids.
h1
A. 100%.
h2
B. 200%.
C. 300%.
D. 700%.
□
24. The ratio of the surface areas of two
similar solids is 25 : 36. Find the ratio of
the volumes of the two solids.
h3
A. 1 : 7 : 19
A. 5 : 6
B. 1 : 8 : 27
B. 25 : 36
C. 1 : 26 : 189
C. 125 : 216
D. 1 : 27 : 216
D. 625 : 1 296
□
25. The following figure shows a right
cylindrical container with the base radius
of 5 cm. After fully immersing 5 metal
balls with diameters of 2 cm each in
water, water does not overflow, find the
rise in water level.
□