Show WorkingWorked example 1: volume of cuboids and prisms
Work out the volume of the cuboid.
- Volume of a cuboid = length × width × height.
- 6 × 4 × 2 = 48 cm³.
Answer 48 cm³
Geometry and measuresFoundation and Higher
Volume and surface area GCSE questions with answers
8 volume and surface area questions to try, each with the answer and the full working one tap away. Every question here was made and worked out by the Show Working maths engine, not typed in by hand.
This topic covers the volume of cuboids, prisms and cylinders, the surface area of cuboids and cylinders, and the volume and surface area of cones, spheres and pyramids. In the exam the formulae for cones and spheres are given to you.
01 / Quiz yourselfTry it, then tap to check
Volume and surface area questions to try
Work each one out on paper first. Then open the answer and compare your working with ours, step by step.
01 / Volume of cuboids and prismsBoth tiers
Work out the volume of the cuboid.
Show the answer and working
- Volume of a cuboid = length × width × height.
- 6 × 8 × 8 = 384 cm³.
Answer 384 cm³
02 / Volume of cuboids and prismsBoth tiers
The diagram shows a prism. The cross-section is a right-angled triangle. Work out the volume of the prism.
Show the answer and working
- Volume of a prism = area of the cross-section × length.
- Area of the triangle = ½ × 9 × 5 = 22.5 cm².
- Volume = 22.5 × 14 = 315 cm³.
Answer 315 cm³
03 / Surface area of a cuboidBoth tiers
Work out the total surface area of the cuboid.
Show the answer and working
- A cuboid has 6 faces, in 3 matching pairs.
- Front and back: 2 × 3 × 2 = 12 m².
- Top and bottom: 2 × 3 × 6 = 36 m².
- The two ends: 2 × 6 × 2 = 24 m².
- Total: 12 + 36 + 24 = 72 m².
Answer 72 m²
04 / Surface area of a cuboidBoth tiers
Work out the total surface area of the cuboid.
Show the answer and working
- A cuboid has 6 faces, in 3 matching pairs.
- Front and back: 2 × 7 × 9 = 126 cm².
- Top and bottom: 2 × 7 × 3 = 42 cm².
- The two ends: 2 × 3 × 9 = 54 cm².
- Total: 126 + 42 + 54 = 222 cm².
Answer 222 cm²
05 / Volume of a cylinderBoth tiers
A cylinder has radius 7 m and height 10 m. Work out its volume. Give your answer to 1 decimal place.
You can use a calculator for this one.
Show the answer and working
- A cylinder is a prism with a circle at each end: volume = area of the circle × height.
- Area of the circle = π × 7² = 153.9380… m².
- Volume = 153.9380… × 10 = 1539.3804…
- To 1 decimal place: 1539.4 m³.
Answer 1539.4 m³
06 / Volume of cones, spheres and pyramidsBoth tiers
A cone has base radius 6 m and perpendicular height 15 m. Work out its volume. Give your answer to 1 decimal place.
Volume of a cone = 13πr2h
You can use a calculator for this one.
Show the answer and working
- Volume = ⅓ × π × 6² × 15 = 565.4867…
- To 1 decimal place: 565.5 m³.
Answer 565.5 m³
07 / Surface area of a cylinderBoth tiers
A closed cylinder has radius 7 cm and height 16 cm. Work out its total surface area. Give your answer to 1 decimal place.
You can use a calculator for this one.
Show the answer and working
- The curved surface opens out into a rectangle. Its length is the circumference, 2 × π × 7, and its width is the height, 16.
- Curved surface = 2 × π × 7 × 16 = 703.7168…
- Each circle end = π × 7² = 153.9380…
- Total = 703.7168… + 2 × 153.9380… = 1011.5928…
- To 1 decimal place: 1011.6 cm².
Answer 1011.6 cm²
08 / Surface area of cones, spheres and pyramidsBoth tiers
A solid hemisphere (half a sphere) has radius 10 cm. Work out its total surface area. Give your answer to 1 decimal place.
Surface area of a sphere = 4πr2
You can use a calculator for this one.
Show the answer and working
- The curved surface is half of a sphere: 4 × π × 10² ÷ 2 = 628.3185…
- The flat face is a circle: π × 10² = 314.1593…
- Total: 628.3185… + 314.1593… = 942.4778…
- To 1 decimal place: 942.5 cm².
Answer 942.5 cm²
02 / What's covered6 kinds of question
Volume and surface area at GCSE and where marks go
- Volume of cuboids and prismsBoth tiers
- Surface area of a cuboidBoth tiers
- Volume of a cylinderBoth tiers
- Volume of cones, spheres and pyramidsBoth tiers
- Surface area of a cylinderBoth tiers
- Surface area of cones, spheres and pyramidsBoth tiers
Worked example 2: surface area of cones, spheres and pyramids
A solid hemisphere (half a sphere) has diameter 30 m. Work out its total surface area. Give your answer to 1 decimal place.
Surface area of a sphere = 4πr2
You can use a calculator for this one.
- The radius is half the diameter: 30 ÷ 2 = 15 m.
- The curved surface is half of a sphere: 4 × π × 15² ÷ 2 = 1413.7167…
- The flat face is a circle: π × 15² = 706.8583…
- Total: 1413.7167… + 706.8583… = 2120.5750…
- To 1 decimal place: 2120.6 m².
Answer 2120.6 m²
A common mistake
Missing faces when finding surface area. A cuboid 2 cm by 3 cm by 4 cm has six faces in three matching pairs, so its surface area is 2 × (6 + 8 + 12) = 52 cm².
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