Mensuration — IGCSE Mathematics - International (0607) questions by topic
Surface area, volume and similar shapes all feature: working out a cube's total surface area, calculating the height of a smaller bottle from a capacity ratio, finding the distance travelled around a circle of given radius, and working out a mass of grass seed from an area calculation.
Find, calculate, work out and show are the command words tested, worth from 1 to 6 marks, across 18 questions from 2025 papers. Because similar-shape and area problems often need an intermediate ratio or formula step, practise laying out each stage of a calculation clearly, then use instant marking to check whether a unit conversion, such as litres to centimetres or grams to kilograms, was applied correctly.
May–June 2025, Paper 11
The diagram shows a cube (NOT TO SCALE) with edges of length 5 cm. A cube has edges of length 5 cm. Work out the total surface area of the cube.
Answer this question and get it marked →May–June 2025, Paper 12
A circle has radius r cm. The area of this circle is 16π cm^2. Work out the value of r.
Answer this question and get it marked →May–June 2025, Paper 13
This shape is made using 3 rectangles (NOT TO SCALE). The shape forms a descending staircase of three rectangles whose tops step down from left to right. The left rectangle has…
Answer this question and get it marked →May–June 2025, Paper 22
In this question all lengths are in centimetres. A solid is made by joining a cuboid to a pyramid (NOT TO SCALE). The diagram shows a square-based cuboid with a square-based…
Answer this question and get it marked →May–June 2025, Paper 23
The diagram (not to scale) shows a sector of a circle with radius 8 cm. The area of the sector is 8π cm^2. The perimeter of the sector is (a + bπ) cm. Find the value of a and the…
Answer this question and get it marked →May–June 2025, Paper 31
The diagram shows a square with a hole in the shape of a circle (not to scale). The length of the side of the square is 16 cm. The diameter of the circle is 15 cm. Show that the…
Answer this question and get it marked →May–June 2025, Paper 32
A shape is drawn on a 1 cm^2 grid. The shape is a hexagon-like figure drawn on the grid: it has a flat top with two square notches cut out of the top edge, vertical sides, and the…
Answer this question and get it marked →May–June 2025, Paper 33
Geeta's garden is a rectangle 15.2 m long and 8.5 m wide. She puts 50 g of grass seed on each square metre of the garden. Work out the mass of grass seed she uses. Give your…
Answer this question and get it marked →This cylinder has diameter 6 cm and length 11 cm. Work out the volume of the cylinder. Give the units of your answer.
Answer this question and get it marked →May–June 2025, Paper 41
The diagram shows a solid cylinder and a solid cone. The radius of the cylinder is 5 cm and its height is 12 cm. The height of the cone is 15 cm. The volume of the cylinder is…
Answer this question and get it marked →These two bottles are mathematically similar. The capacity of the small bottle is 0.5 litres. The capacity of the large bottle is 1 litre. The height of the large bottle is 25 cm.…
Answer this question and get it marked →May–June 2025, Paper 42
The diagram shows a wooden cuboid (not to scale) with a cylinder removed. The cuboid has length 22 cm, width x cm and height x cm. The cylinder has length 22 cm and diameter 5 cm,…
Answer this question and get it marked →May–June 2025, Paper 43
The volume of a sphere is 96.5 cm^3. Calculate the radius of the sphere. [Volume of a sphere of radius r: V = (4/3)pir^3]
Answer this question and get it marked →A solid is formed from a cone and a hemisphere. The cone and the hemisphere each have a radius of 6 cm. The cone has a height of 15 cm. The flat circular face of the hemisphere is…
Answer this question and get it marked →The diagram shows two solids (each a frustum-shaped bowl) that are mathematically similar; the large one is on the left and the small one on the right. The volume of the large…
Answer this question and get it marked →May–June 2025, Paper 62
Stage 1. The athlete rotates the hammer holding it by the handle. The hammer travels along a circle of radius 1.8 m. The circumference, C, of a circle of radius r is C = 2pir.…
Answer this question and get it marked →Other IGCSE Mathematics - International topics
- Algebra (75)
- Number (70)
- Statistics (21)
- Geometry (20)
- Functions (14)
- Trigonometry (14)
- Coordinate geometry (8)
- Vectors and transformations (8)
- Sets (6)
- Probability (5)