1
1
A box, in the shape of a cuboid, has volume 357 cm3.
It has a length of 8.5 cm and a width of 6 cm.
Calculate the height of the box.
................................................... cm
[2]
[Total: 2]
2
Find the radius of a hemisphere of volume 80 cm3.
[The volume, V, of a sphere with radius r is
.]
................................................... cm
[3]
[Total: 3]
2
3
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]
3
4
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]
5
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4m
0.45 m
The diagram shows a horizontal container for water with a uniform cross-section.
The cross-section is a semicircle.
The radius of the semicircle is 0.45 m and the length of the container is 4 m.
4
(a) Calculate the volume of the container.
................................................... m3
[2]
(b)
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0.3 m
The greatest depth of the water in the container is 0.3 m.
The diagram shows the cross-section.
Calculate the number of litres of water in the container.
Give your answer correct to the nearest integer.
................................................... litres
[6]
[Total: 8]
5
6
O
R
X
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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
An empty fuel tank is filled using a cylindrical pipe with diameter 8 cm.
Fuel flows along this pipe at a rate of 2 metres per second.
It takes 24 minutes to fill the tank.
Calculate the capacity of the tank.
Give your answer in litres.
................................................... litres
[4]
[Total: 4]
6
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]
7
9
The total perimeter of a semicircle is 19.02 cm.
Calculate the radius of the semicircle.
................................................... cm
[3]
[Total: 3]
10
The diagram shows a sector of a circle of radius 8 cm.
The length of the arc PQ is 6.4 cm.
Find the area of the sector.
................................................... cm2
[4]
8
[Total: 4]
11
Calculate the area of the sector of a circle with radius 65 mm and sector angle 42°.
Give your answer in square centimetres.
................................................... cm2
[3]
[Total: 3]
12
The diagram shows the net of a triangular prism on a 1 cm2 grid.
9
(a) Write down the mathematical name for the type of triangle shown on the grid.
(b)
(i)
...................................................
[1]
................................................... cm
[1]
Measure the perpendicular height of the triangle.
10
(ii) Calculate the area of the triangle.
................................................... cm2
[2]
................................................... cm3
[2]
(iii) Calculate the volume of the triangular prism.
[Total: 6]