1
1
The diagram shows a field ABCDE.
(a) Calculate the perimeter of the field ABCDE.
................................................... m
[4]
Angle ABD = ...................................................
[4]
(b) Calculate angle ABD.
2
(c)
(i)
Calculate angle CBD.
Angle CBD = ...................................................
[2]
...................................................
[2]
................................................... hectares
[4]
(ii) The point C is due north of the point B.
Find the bearing of D from B.
(d) Calculate the area of the field ABCDE.
Give your answer in hectares.
[1 hectare = 10 000 m2]
[Total: 16]
2
The diagram shows a cone with radius 1.75 cm and height 6 cm.
3
(a) Calculate the total surface area of the cone.
[The curved surface area, A, of a cone with radius r and slant height l is
.]
................................................... cm2
[5]
(b)
The cone contains salt to a depth of 4.5 cm.
The top layer of the salt forms a circle that is parallel to the base of the cone.
(i)
Show that the volume of the salt inside the cone is 18.9 cm3, correct to 1 decimal place.
[The volume, V, of a cone with radius r and height h is
.]
[4]
4
(ii) The salt is removed from the cone at a constant rate of 200 mm3 per second.
Calculate the time taken for the cone to be completely emptied.
Give your answer in seconds, correct to the nearest second.
................................................... s
[3]
[Total: 12]
3
ABCDEFGH is a regular octagon with sides of length 6 cm.
The diagram shows part of the octagon.
O is the centre of the octagon and M is the midpoint of AB.
A
M
B
NOT TO
SCALE
O
(a)
(i)
Show that angle OAM is 67.5°.
[2]
5
(ii) Calculate the area of the octagon.
................................................... cm2
[4]
(b) Find the area of the circle that passes through the vertices of the octagon.
................................................... cm2
[3]
[Total: 9]
6
4
O
R
X
NOT TO
SCALE
4 cm
P
11 cm
Q
The diagram shows a rectangle OPQR with length 11 cm and width 4 cm.
OQ is a diagonal and OPX is a sector of a circle, centre O.
Calculate the percentage of the rectangle that is shaded.
................................................... %
[5]
[Total: 5]
7
5
The diagram shows a square with vertices on the circumference of a circle, centre O.
The radius of the circle is 6 cm.
Work out the shaded area.
................................................... cm2
[5]
[Total: 5]
8
6
The diagram shows a solid metal shape made from a cone and a hemisphere, both with radius 6.2 cm.
The total surface area of the solid shape is 600 cm2.
Calculate the slant height, l, of the cone.
[The surface area, A, of a sphere with radius r is
.]
[The curved surface area, A, of a cone with radius r and slant height l is
.]
l = ................................................... cm
[4]
[Total: 4]
9
7
The diagram shows a square ABCD with side length k cm.
MDE is a sector of a circle, centre D.
E lies on the diagonal, BD, of the square.
M is the midpoint of AD.
Find the percentage of the square that is shaded.
................................................... %
[4]
[Total: 4]
10
8
NOT TO
SCALE
The diagram shows a circle inside a square.
The circle touches the four sides of the square.
The area of the square is 81 cm2.
Calculate the shaded area.
................................................... cm2
[4]
[Total: 4]
11
9
NOT TO
SCALE
9 cm
4 cm
The diagram shows a toy.
The shape of the toy is a cone, with radius 4 cm and height 9 cm, on top of a hemisphere with radius 4 cm.
Calculate the volume of the toy.
Give your answer correct to the nearest cubic centimetre.
[The volume, V, of a cone with radius r and height h is
[The volume, V, of a sphere with radius r is
.]
.]
Answer ........................................................................cm3
[4]
[Total: 4]
12
10
The diagram shows a circle with a diameter of 7 cm and a parallelogram with a base of 12 cm.
The circle touches two of the sides of the parallelogram.
Calculate the shaded area.
................................................... cm2
[3]
[Total: 3]
13
11
C
NOT TO
SCALE
6 cm
O
B
5 cm
A
The diagram shows a shape made from a quarter-circle, OAB, and a right-angled triangle OBC.
The radius of the circle is 5 cm and OC = 6 cm.
Calculate the area of the shape.
................................................... cm2
[3]
[Total: 3]