REVIEW-Surface Area & Volume
Karen
is
painting
the
outside
of
her
birdhouse. She needs to calculate how much
18.03 cm
paint is needed. The birdhouse has a square
base.

The shaded hole has a diameter of 6 cm.

The edge of the roof is 18.03 cm.
What is the total surface area of her
6 cm
30 cm
birdhouse?
20 cm
20 cm
A water reservoir is in the shape of a cylinder that is capped at either end by a
hemisphere.
6.4 m
2.4 m
How many litres of water are in the cylinder if it is
2
full?
3
A gazebo is in the shape of a right prism. Its roof is
8.5 m
pyramid shaped.
Students have been hired to paint the walls, the roof,
and the door of the gazebo.
Each floor side is 8m long, the walls are 3m high and
the ridges of the roof are 8.5m long.
Calculate the surface area to be painted.
A blimp is formed from a hemisphere, a right cylinder
and a right cone.
What is the surface area of this huge "pencil"
blimp?
3m
8m
REVIEW-Surface Area & Volume
The total area of a square prism whose
base measures 6 cm a side is 312 cm2.
What is the height of the prism?
6 cm
6 cm
A tank is in the shape of a right cylinder whose height is 20 m. The tank can hold
6280kL of oil. What is the length of the diameter of this tank?
The volume of a square-based pyramid is 223 cm3.
The
height of this pyramid is 12 cm. What is the length of a side
of the base of this pyramid?
What is the total surface area of the following solid?
15 cm
9 cm
25 cm
12 cm
REVIEW-Surface Area & Volume
A maritime shipping company has to
repaint all its rusted buoys.
2.2 m
If 1 litre of paint covers 10 m2, how
2m
much paint is needed to repaint each
buoy?
2.5 m
1.8 m
A box, in the shape of a square prism
topped by a right pyramid, has a volume of
728 cm3. What is the total height of this
8.6 cm
box?
12 cm
Julie bought a 2.4-litre box of laundry detergent. The box is in the shape of a
rectangular prism in which the base measures 15 cm by 10 cm.
When she got home, she emptied the contents of the box into cylindrical containers, 10
cm in diameter. The containers are half the height of the box. How many containers
will she need to use?
REVIEW-Surface Area & Volume
A buoy has been taken out of a river to be
h = 120 cm
r = 40 cm
repainted. This buoy is made up of a
hemisphere topped by a cone.
h
Which of the following measures is the
best approximation of the total area of this
r
buoy?
The volume of the adjacent right pyramid with
a square base is 1296 cm3. The sides of the
base measure 18 cm. What is the lateral
h
area of this pyramid?
a
18 cm
The lateral area of a cube is equal to the total area of a cylinder having a 5 cm radius
and a height of 20 cm. What is the volume of this cube?
What surface area of cardboard would
be needed to make this pyramid?
Apothem = 9 cm
10 cm
10 cm
The solid is made up of a prism with a right triangle as
its base. A right pyramid sits on top of the prism. The
base of the right pyramid is congruent to that of the
prism. What is the volume of this solid?
Note 1 cm3 of ice weighs 0.98 g.
10 m
6m
REVIEW-Surface Area & Volume
David's Scout Group drank 50 containers of
juice. How many litres of juice did the
group drink?
12 cm
4 cm
6 cm
A cylindrical rim has been added to the
traditional cone-shaped base.
To price their new cone, they need to know
the amount of ice cream that will be used to
fill the entire cone as well as the hemispheric
scoop atop the cone.
How many cm3 of ice cream will be
needed?
A manufacturer sells tents of different sizes.
One
of
them
has
the
shape
of
h
a
hemisphere, as shown on the right.
Its lateral area is 9.05 m2.
To the nearest tenth, what is the height h of the tent?
The solid on the right consists of a cube
topped by a pyramid.
The side of the cube measures 12 cm.
The total height of the solid measures
20 cm
20cm. Find the volume of this solid.
12 cm
REVIEW-Surface Area & Volume
The figure to the right shows a pyramid
S
within a cube.
The total surface area of the cube is 600
cm2. Vertex S of the pyramid is at the
centre of the top face of the cube.
Find the total surface area of the
pyramid after it is removed from the
cube.
The pencil container shown on the right has
a volume of 565cm3. The diameter of the
base is 6cm. The length of the cylindrical
part is 18 cm.
?
18 cm
6 cm
To the nearest centimetre, what is the full length the container?
A painter uses a roller with a diameter of 6 cm. Each revolution covers an area of 471
cm2. What is the width of the roller to the nearest cm?
width
6 cm
REVIEW-Surface Area & Volume
An industrial drill bit was used to drill a hole, the side view of which is pictured in the
diagram below. It takes 25 mL of glue to fill this hole.
5 cm
What is the diameter of the hole's opening?
Dean wants to make a Santa Claus hat. He bought some white fur material for the 10cm wide band and red material for the rest of the cone-shaped hat. The apothem of the
cone section is 10 cm and the perimeter of Dean’s head is 80 cm.
How many m2 of material will he need to buy to make the hat?
Mexico's largest pyramid has a square base. Its lateral area is 0.2 km2 and its apothem
measures 266 m. During carnival festivities, a brightly lit star is placed at the top of the
pyramid.
How many metres from the ground is this star?
266 m
REVIEW-Surface Area & Volume
All the stores of a certain shoe company are built
in the shape of a cube with a right square
pyramid on top.
The side of the cube is 20metres.
The total volume of the building is 8800 m3.
What is the height of the pyramid?
20 m
The box on the right in the shape of a rectangular
20 cm
prism has a width of 20cm, a length of 36cm, and
an unknown height.
36 cm
The volume of the box is 7200 cm3.
What is the total surface area of the box?
A capsule is in the shape of a cylinder with hemispheres at each
end. The capsule's total length is 14 mm and its diameter is
5mm. Find the volume of the capsule.
A torpedo is made up of a cylinder and a hemisphere.
What is the total area of this torpedo expressed in cm2, rounded to the nearest
hundredth?
REVIEW-Surface Area & Volume
An engineer is trying to determine the
heating and air conditioning needs of a
48 m
building in the shape of a right triangular
prism.
The building has a volume of 32 640 m3. It is
17 storeys high.
What is the distance, in metres, between
each storey?
h
52 m
The body and nose of her rocket are built
using a cylinder attached to a cone.
For the rocket to fly Tania knows that:

30 cm
The cylinder and the cone must have the
same diameter.

The cone's height must not be more than
4 cm
25% of the cylinder's height.
The cylinder has a diameter of 4 cm and a height of 30 cm.
What is the greatest lateral surface area that the rocket can have?
REVIEW-Surface Area & Volume
Sixteen cylindrical neon tubes, each 90 cm
20 cm
long, are tightly packed in a box in the
20 cm
shape of a square prism.
To protect the tubes, foam is injected into
the empty space in the box.
What volume of foam is required to
90 cm
completely fill the empty space?
Edward loves astronomy. For his birthday, Edward’s
mother made him a cake in the shape of a rocket
15 cm
(a cylinder with a cone on top). What is the total
volume of Edward’s birthday cake?
8 cm
24 cm
2
The total surface area of the probe is 179m and the radius of its base measures 3m.
What is the total height of Space Probe
Mars 3?
?
3m
REVIEW-Surface Area & Volume
Daniel baked a birthday cake for his friend Lisa. The cake is in the form of a cylinder
with radius 15 cm. Daniel iced the cake with 200 g of icing. What is the height of the
cake to the nearest hundredth? Note 1g of icing covers 10cm2 of cake.
The diameter of the test tube shown below is 2.2 cm
d = 2.2 cm
and its volume is 56 cm3.
What is the height of the test tube?
V = 56 cm3
h=?
A block of modelling clay, in the shape of a right prism. It measures 40 cm by 15 cm by
15 cm.
15 cm
15 cm
40 cm
All the clay from the prism is used to construct a cone. The diameter of the cone is
20cm.
h
20 cm
What is the height of the cone to the nearest centimetre?
REVIEW-Surface Area & Volume
Two litres of cake batter is poured into a cake mould in the shape of a regular
hexagonal prism.
The measure of one side of the base of the prism is 9.6 cm and the apothem measures
8.3 cm.
2L
9.6 cm
8.3 cm
What will be the height of the cake batter in the cake mould?
A maple syrup producer collects sap from the
1.2 m
trees and stores it in a large tank.
The lower portion of the tank is a half-cylinder,
while the upper portion is a right prism. Both
sections have the same height.
The lower portion of the tank can hold 1.98m3
of maple sap.
What volume of sap can the tank hold when full?
A tank is in two sections, as shown in the diagram.
The bottom section of the tank is a cube with sides
measuring 140cm. The top section of the tank is a
80 cm
140 cm
cylinder, which has a height of 80 cm, and a radius of
25cm.
Calculate the volume of the tank, and use this volume to find the capacity in litres
of the tank.