Topical Worksheets for Cambridge O LEVEL
Mathematics D (4024)
Mensuration
1st edition, for examination until 2025
1
1 A cone has radius 4.5 cm and height 10.4 cm.
Calculate, in terms of , the volume of the cone.
[The volume, V, of a cone with radius r and height h is .]
................................................... cm3 [2]
[Total: 2]
2 Rectangle A measures 3 cm by 8 cm.
Five rectangles congruent to A are joined to make a shape.
Work out the perimeter of this shape.
................................................... cm [2]
[Total: 2]
2
Calculate the area of the trapezium.
................................................... cm2 [2]
[Total: 2]
4 Change 5.3 kilometres into metres.
................................................... m [1]
[Total: 1]
3
5 A solid cylinder has radius 3 cm and height 4.5 cm.
Calculate the total surface area of the cylinder.
................................................... cm2 [4]
[Total: 4]
6 The total perimeter of a semicircle is 19.02 cm.
Calculate the radius of the semicircle.
................................................... cm [3]
[Total: 3]
4
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]
[Total: 4]
5
The diagram shows a cuboid.
Calculate the volume of the cuboid.
................................................... cm3 [1]
[Total: 1]
9 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]
10 The diagram shows the net of a triangular prism on a 1 cm2 grid.
6
(a) Write down the mathematical name for the type of triangle shown on the grid.
................................................... [1]
(b) (i) Measure the perpendicular height of the triangle.
................................................... cm [1]
7
(ii) Calculate the area of the triangle.
................................................... cm2 [2]
(iii) Calculate the volume of the triangular prism.
................................................... cm3 [2]
[Total: 6]
11
The diagram shows a circle, centre O, radius 11 cm.
C, F, G and H are points on the circumference of the circle.
The line AD touches the circle at C and is parallel to the line EG.
8
B is a point on AD and angle ABO = 140°.
(a) Write down the mathematical name of the straight line AD.
................................................... [1]
(b) (i) Find, in terms of , the circumference of the circle.
................................................... cm [2]
(ii) Work out angle FOH.
Angle FOH = ................................................... [2]
(iii) Calculate the length of the minor arc FH.
................................................... cm [2]
(c) (i) Give a reason why angle BCO is 90°.
...................................................................................................................................... [1]
(ii) Show that BC = 13.11 cm, correct to 2 decimal places.
[3]
9
(iii) Calculate BH.
BH = ................................................... cm [3]
[Total: 14]
12 A cube has a surface area of 384 cm2.
Find the length of one of its sides.
................................................... cm [3]
[Total: 3]
10
13
The diagram shows a right-angled triangular prism.
Work out the volume of the prism.
................................................... cm3 [3]
[Total: 3]
14
The diagram shows a rectangular patio with sides 6 m and 8 m.
(a) Work out the perimeter of the patio.
................................................... m [1]
11
(b) Henri covers the patio floor with square tiles.
The tiles are 0.5 m by 0.5 m.
Work out the number of tiles he needs.
................................................... [2]
[Total: 3]
15 The diagram shows the net of a solid on a 1 cm2 grid.
(a) Write down the mathematical name for the solid.
................................................... [1]
(b) Work out the volume of the solid.
................................................... cm3 [2]
[Total: 3]
16 The diagram shows a line AB on a 1 cm2 grid.
12
(a) Write down the coordinates of point A.
( .................... , .................... ) [1]
(b) Write down the vector .
[1]
(c)
Mark point C on the grid. [1]
(d) (i) Work out .
[1]
(ii) Complete this statement.
[1]
(e) A, B and C are three vertices of a parallelogram, ABCD.
13
(i) Mark point D on the diagram and draw the parallelogram ABCD. [1]
(ii) Work out the area of the parallelogram.
Give the units of your answer.
.............................. .................... [2]
[Total: 8]
17
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]
14
18
The diagram shows a semicircle with diameter AC.
B is a point on the circumference and AB = BC.
Work out the area of triangle ABC.
................................................... cm2 [3]
[Total: 3]
19 A square has perimeter 12x.
Find an expression, in terms of x, for the area of the square.
Give your answer in its simplest form.
................................................... [3]
[Total: 3]
15
20
The diagram shows a sector of a circle with centre O, radius 8 cm and sector angle 165°.
(a) Calculate the total perimeter of the sector.
................................................... cm [3]
(b) The surface area of a sphere is the same as the area of the sector.
Calculate the radius of the sphere.
[The surface area, A, of a sphere with radius r is .]
................................................... cm [4]
16
(c)
A cone is made from the sector by joining OA to OB.
(i) Calculate the radius, r, of the cone.
r = ................................................... cm [2]
(ii) Calculate the volume of the cone.
[The volume, V, of a cone with radius r and height h is .]
................................................... cm3 [4]
[Total: 13]
17
21 A cylinder with radius 6 cm and height h cm has the same volume as a sphere with radius 4.5 cm.
Find the value of h.
[The volume, V, of a sphere with radius r is .]
h = ................................................... [3]
[Total: 3]
22 A solid metal cube of side 20 cm is melted down and made into 40 solid spheres, each of radius r cm.
Find the value of r.
[The volume, V, of a sphere with radius r is .]
r = ................................................... [3]
[Total: 3]
18
23
A solid cylinder has radius x cm and height cm.
The surface area of a sphere with radius R cm is equal to the total surface area of the cylinder.
Find an expression for R in terms of x.
[The surface area, A, of a sphere with radius r is .]
R = ................................................... [3]
[Total: 3]
19
24
Water flows at a speed of 20 cm/s along a rectangular channel into a lake.
The width of the channel is 15 cm.
The depth of the water is 2.5 cm.
Calculate the amount of water that flows from the channel into the lake in 1 hour.
Give your answer in litres.
................................................... litres [4]
[Total: 4]
20
25
The diagram shows a cuboid measuring 15 cm by 12 cm by 4 cm.
Calculate the surface area of the cuboid.
................................................... cm2 [3]
[Total: 3]
26 Calculate the area of a circle with radius 12 cm.
................................................... cm2 [2]
[Total: 2]
27 Change 4.6 metres to centimetres.
................................................... cm [1]
[Total: 1]
28 Complete the statements.
3.5 kg = ......................................... g
1.4 m2 = ......................................... cm2 [2]
[Total: 2]
21
29
The diagram shows two sectors of circles with the same centre.
Calculate the shaded area.
................................................... cm2 [3]
[Total: 3]
22
30 A pipe is completely full of water.
Water flows through the pipe at a speed of 1.2 m/s into a tank.
The cross-section of the pipe has an area of 6 cm2.
Calculate the number of litres of water flowing into the tank in 1 hour.
................................................... litres [4]
[Total: 4]
31 Soraya makes rectangular flags.
(a) On the rectangle, draw the lines of symmetry. [2]
(b) Each flag measures 1.2 m by 1.8 m.
Calculate the area of one flag.
................................................... m2 [2]
[Total: 4]
32 A cuboid measures 5 cm by 4 cm by 2 cm.
23
(a) Calculate the volume of this cuboid.
Give the units of your answer.
.............................. .................... [3]
(b) On the 1 cm2 grid, draw an accurate net of this cuboid.
One face has been drawn for you.
[3]
[Total: 6]
24
33 The length of the edge of a cube is 8 cm.
Calculate the surface area of this cube.
................................................... cm2 [2]
[Total: 2]
34
Calculate the area of this triangle.
................................................... cm2 [2]
[Total: 2]
35 Change 4365 metres into centimetres.
................................................... cm [1]
[Total: 1]
36 Change 3670 centimetres to metres.
................................................... m [1]
[Total: 1]
25
37 The volume of a cuboid is 180 cm3.
The base is a square of side length 6 cm.
Calculate the height of this cuboid.
................................................... cm [2]
[Total: 2]
38
The diagram shows a semicircle with diameter 9 cm.
Calculate the total perimeter of this semicircle.
................................................... cm [3]
[Total: 3]
39 A closed box in the shape of a cuboid has length 5 cm, width 4 cm and height 2 cm.
Calculate the volume of the box.
................................................... cm3 [2]
[Total: 2]
26
40 The diagram shows a solid cuboid made of identical cubes.
Work out the number of cubes in the cuboid.
................................................... [1]
[Total: 1]
