Mensuration — IGCSE Mathematics (0580) questions by topic
Mensuration questions ask you to find the total surface area of a cuboid from three given dimensions, calculate a semicircle's area from its radius, work out the area of an irregular shape drawn on a centimetre-squared grid, and calculate the perimeter of a major sector once the removed minor sector's angle is known. Calculate, find, work out, deduce and state require choosing the right formula for the shape shown, not just any area or perimeter rule.
54 questions from 2023 to 2025 sit here, worth from 1 to 16 marks. Because unit slips, such as forgetting to add a curved edge to a sector's perimeter, are easy to make under time pressure, submitting each answer for instant marking catches a missed edge or a wrongly squared radius at once, instead of it costing marks silently across several similar questions.
May–June 2025, Paper 11
Calculate the volume of a cube with side length 3cm.
Answer this question and get it marked →May–June 2025, Paper 12
The diagram shows a point P and three triangles, A, B and C, on a 1 cm^2 grid. Find the area of triangle B.
Answer this question and get it marked →The diagram shows a shape made from two different semicircles, with the same centre. (NOT TO SCALE.) A small semicircle of radius 4 cm sits above a horizontal diameter line, and a…
Answer this question and get it marked →May–June 2025, Paper 13
The diagram shows two faces of a net of a cuboid on a 1 cm² grid. The two drawn faces together form a 6 cm by 2 cm rectangle divided into two 3 cm by 2 cm faces. Complete the…
Answer this question and get it marked →The diagram shows the net of a square-based pyramid. The perpendicular height of each triangle is 4 cm. The base has side length 5 cm. Calculate the surface area of the pyramid.
Answer this question and get it marked →The diagram shows a trapezium. The two parallel sides are 4 cm and 10 cm, and the perpendicular distance between them is h cm. The area of the trapezium is 42 cm². Work out the…
Answer this question and get it marked →The diagram shows a sector of a circle with radius 3 cm and sector angle 60°. Calculate the area of the sector. Give your answer in terms of pi in its simplest form.
Answer this question and get it marked →May–June 2025, Paper 21
The diagram shows solid A and solid B. Solid A is made from a hemisphere and a cone each with radius 6 cm. The cone has sloping edge 10 cm. Solid B is a cylinder with radius 4 cm…
Answer this question and get it marked →May–June 2025, Paper 22
The diagram (NOT TO SCALE) shows a sector of a circle, centre O. The two radii have length 18 cm and the angle at O between them is 45 degrees. The length of the arc is npi cm.…
Answer this question and get it marked →The diagram (NOT TO SCALE) shows a solid made by joining a hemisphere to a cylinder. The radius of both the hemisphere and the cylinder is 6 cm. The height of the cylinder is 5…
Answer this question and get it marked →May–June 2025, Paper 23
The diagram (NOT TO SCALE) shows a sector of a circle, centre O. The radius of the circle is 6 cm. The minor sector angle AOB is 40° (A above B, both on the circle). Calculate the…
Answer this question and get it marked →May–June 2025, Paper 31
The diagram shows a shape made from a square and four congruent isosceles triangles (NOT TO SCALE). The square has side 7.8 cm. One isosceles triangle is attached to each side of…
Answer this question and get it marked →The volume of a cylinder is 863.5 cm^3. The height of the cylinder is 12.3 cm. Find the radius of the cylinder. ............ cm
Answer this question and get it marked →A bar of gold in the shape of a cuboid has dimensions 2 cm by 4 cm by 6.5 cm. The density of gold is 19.32 g/cm^3. Calculate the mass of this bar of gold. [Density = mass /…
Answer this question and get it marked →The diagram shows a shape made from a rectangle and a semicircle (NOT TO SCALE). The rectangle is 16 cm wide and 9 cm high. A semicircle of diameter 10 cm sits on the top edge of…
Answer this question and get it marked →May–June 2025, Paper 32
A sphere has radius 8 cm. A cone has radius 8 cm and height h. The sphere and the cone have the same volume. Work out the height, h, of the cone.
Answer this question and get it marked →May–June 2025, Paper 33
The diagram shows a solid cylinder with height 10 cm. The volume of the cylinder is 478 cm^3. Find the radius of the cylinder.
Answer this question and get it marked →May–June 2025, Paper 41
A warehouse has a floor area of 800 m^2. The plan of the warehouse is drawn to a scale of 1 : 50. Calculate the floor area on the plan. Give your answer in square centimetres.
Answer this question and get it marked →The diagram (not to scale) shows a major sector of a circle with radius 7.5 cm. The angle of the removed minor sector at the centre is 126°, so the major sector has an angle of…
Answer this question and get it marked →May–June 2025, Paper 42
The diagram shows a trapezium ABCD (not to scale). DC = 10 cm is the top parallel side and AB = 12 cm is the bottom parallel side. The perpendicular distance between the two…
Answer this question and get it marked →A solid wooden cone has base radius 4 cm and height 12 cm. The density of the wood is 0.74 g/cm^3. Calculate the mass of the cone. [Density = Mass ÷ Volume]
Answer this question and get it marked →May–June 2025, Paper 43
The diagram shows a pentagon made from two congruent trapeziums (NOT TO SCALE). The pentagon has a flat horizontal base of width 14 cm and is symmetrical about a vertical line.…
Answer this question and get it marked →The diagram shows a solid cuboid with sides of length 4.5 cm, 8 cm and 13.2 cm (NOT TO SCALE). Calculate the volume of the cuboid.
Answer this question and get it marked →The diagram shows an equilateral triangle ABC with all sides of length 12 cm (NOT TO SCALE). With A at the top apex, B at the bottom right and C at the bottom left, base CB = 12…
Answer this question and get it marked →The diagram shows a frustum made by removing a small cone from a large cone (NOT TO SCALE). The frustum is shown as the upper part (wider top, narrower bottom) with the removed…
Answer this question and get it marked →May–June 2023, Paper 11
Calculate the volume of a sphere with diameter 4.8 cm. [The volume, V, of a sphere with radius r is V = (4/3)πr³.]
Answer this question and get it marked →May–June 2023, Paper 12
The diagram shows a right-angled triangular prism with triangle sides 3 cm, 4 cm, 5 cm and length 6 cm. On the 1 cm² grid, complete the net of this prism. One face has been drawn…
Answer this question and get it marked →May–June 2023, Paper 13
The diagram shows a cuboid with dimensions 8 cm, 3 cm and 5 cm. Find the total surface area of the cuboid.
Answer this question and get it marked →The diagram shows a triangular prism whose cross-section is a triangle with base 4 cm and height 2 cm, and the prism length is 4 cm (with a 4 cm slant edge shown). On the 1 cm²…
Answer this question and get it marked →May–June 2023, Paper 21
Calculate the volume of a sphere with diameter 4.8 cm. [The volume, V, of a sphere with radius r is V = (4/3)πr³.]
Answer this question and get it marked →May–June 2023, Paper 22
The diagram shows a shape ABCD formed by the sectors of two circles with the same centre O. Both sector angles are 140°, OC = 3.2 cm and CB = 2.6 cm. The area of the shape is kπ…
Answer this question and get it marked →May–June 2023, Paper 23
The diagram shows a cuboid with dimensions 8 cm, 3 cm and 5 cm. Find the total surface area of the cuboid.
Answer this question and get it marked →The volume of a cylinder is 1970 cm³. The height of the cylinder is 12.8 cm. Calculate the radius of the cylinder.
Answer this question and get it marked →May–June 2023, Paper 31
The diagram shows a right-angled triangle ABC and a semicircle. The radius of the semicircle is 4.5 cm. AC = 8.9 cm and BC = 13.2 cm. Calculate the shaded area. Give the units of…
Answer this question and get it marked →May–June 2023, Paper 32
A rectangle has an area of 12 cm² and a perimeter of 16 cm. A shape is made from six of these rectangles. Find the area and perimeter of this shape.
Answer this question and get it marked →May–June 2023, Paper 33
The diagram shows a shape on a 1 cm² grid. Work out the area of the shape.
Answer this question and get it marked →May–June 2023, Paper 41
The diagram shows a solid triangular prism ABCDEF of length 15 cm. AB = 6.4 cm, EB = 5.7 cm and the volume of the prism is 145 cm³. Show that angle EBA = 32°, correct to the…
Answer this question and get it marked →The diagram shows a right-angled triangle PQR with PQ = 8 cm and QR = 24 cm (right angle at Q). Calculate the area of triangle PQR.
Answer this question and get it marked →May–June 2023, Paper 42
A cone has base diameter 8 cm and perpendicular height 15 cm. NOT TO SCALE. Calculate the volume of the cone. [The volume, V, of a cone with radius r and height h is V =…
Answer this question and get it marked →May–June 2023, Paper 43
The diagram shows a shape made from a square ABCD and two equal sectors of a circle. The square has side 11 cm. MAB and DCN are straight lines. NOT TO SCALE. Calculate the area of…
Answer this question and get it marked →October–November 2023, Paper 11
The circumference of a circle is 59 cm. Calculate the radius of the circle.
Answer this question and get it marked →The diagram shows a trapezium with parallel sides 8 cm and 14 cm and a perpendicular height of 6 cm. NOT TO SCALE. Find the area of this trapezium.
Answer this question and get it marked →Calculate the area of a semicircle with radius 10 cm.
Answer this question and get it marked →October–November 2023, Paper 13
The surface area of a cube is 73.5 cm². Find the length of one side of the cube.
Answer this question and get it marked →The diagram shows a sector of a circle with radius r cm and sector angle 72°. The arc length is 9.35 cm. NOT TO SCALE. Calculate the value of r.
Answer this question and get it marked →October–November 2023, Paper 21
ABCD is a rhombus with side length 13.6 cm. Angle ABC = 41°. BAC is a sector of a circle with centre B. DAC is a sector of a circle with centre D. NOT TO SCALE. Calculate the…
Answer this question and get it marked →October–November 2023, Paper 22
A solid cylinder has radius 5 cm and height 8 cm. Calculate the total surface area of the cylinder.
Answer this question and get it marked →October–November 2023, Paper 23
A bronze sphere has radius 3.6 cm. The density of bronze is 8.05 g/cm³. Find the mass of the sphere. Give your answer in kilograms, correct to the nearest gram. [The volume, V, of…
Answer this question and get it marked →A cylinder with height 12.5 cm has a curved surface area of 105π cm². Calculate the volume of the cylinder.
Answer this question and get it marked →October–November 2023, Paper 33
The diagram shows a semicircle with diameter AB. O is the midpoint of AB and C is a point on the circumference. AC = 9.6 cm and BC = 18 cm. NOT TO SCALE. Calculate the area of…
Answer this question and get it marked →October–November 2023, Paper 41
The diagram shows a solid formed by joining two hemispheres and a cylinder. The radius of the large hemisphere is 5.4 cm. The radius of the small hemisphere and the radius of the…
Answer this question and get it marked →October–November 2023, Paper 42
The diagram shows a sector of a circle that is made into a cone by joining OA to OB. The sector angle is x° and the radius of the sector is 7.5 cm. The base radius of the cone is…
Answer this question and get it marked →Other IGCSE Mathematics topics
- Number (230)
- Algebra and graphs (150)
- Geometry (93)
- Statistics (52)
- Trigonometry (33)
- Transformations and vectors (32)
- Probability (27)
- Coordinate geometry (16)