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Year 9 · Key Stage 3 · free KS3 maths worksheet

Surface area and volume

14 original questions, 58 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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The questions

1

The diagram shows a cuboid.

  1. Work out the volume of the cuboid.
  2. Work out the total surface area of the cuboid.
8 cm3 cm5 cm
4 marks
Show answer
a) 120 cm³ b) 158 cm²
2

A cube has a volume of 64 cm3.

Work out the total surface area of the cube.

3 marks
Show answer
96 cm²
3
  1. A prism has a cross-section with an area of 24 cm2. The prism is 15 cm long. Work out the volume of the prism.
  2. Another prism has a volume of 540 cm3. Its cross-section has an area of 72 cm2. Work out the length of this prism.
3 marks
Show answer
a) 360 cm³ b) 7.5 cm
4

The cross-section of a triangular prism is a right-angled triangle with base 3 cm, height 4 cm and hypotenuse 5 cm.

The length of the prism is 10 cm.

Work out the total surface area of the prism.

3 cm4 cm10 cm5 cm
3 marks
Show answer
132 cm²
5
  1. Change 5 litres to cm3.
  2. Change 3 m3 to cm3.
  3. Change 4500 cm3 to litres.
  4. Change 2.5 cm3 to mm3.
4 marks
Show answer
a) 5000 cm³ b) 3000000 cm³ c) 4.5 litres d) 2500 mm³
6

A fish tank is a cuboid with a base measuring 40 cm by 25 cm and a height of 20 cm.

The tank is filled with water to a depth of 15 cm.

All of the water is poured into cups. Each cup holds 250 ml.

Work out the number of cups that can be completely filled.

1 ml = 1 cm3

4 marks
Show answer
60
7

The cross-section of a prism is an L-shape.

The L-shape is made by starting with a rectangle 12 cm wide and 9 cm tall, then removing a 7 cm by 5 cm rectangle from the top right corner.

The length of the prism is 24 cm.

Show that the volume of the prism is 1752 cm3.

12 cm7 cm5 cm9 cm24 cmDiagram NOT accurately drawn
5 marks
Show answer
Cross-section area = 12 × 9 - 7 × 5 = 108 - 35 = 73 cm²; volume = 73 × 24 = 1752 cm³
8

A skip is a prism. Its cross-section is a trapezium.

The diagram shows the measurements of the skip.

  1. Work out the volume of the skip.
  2. Callum fills the skip with garden rubbish. Each wheelbarrow load is 0.25 m3. How many wheelbarrow loads fill the skip?
2 m3 m1.5 m1.2 mDiagram NOT accurately drawn
4 marks
Show answer
a) 4.5 m³ b) 18
9

A water tank is a cuboid measuring 1.5 m by 0.8 m by 0.6 m.

The tank is empty. Dev fills the tank completely with water.

Water costs £1.25 for every 100 litres.

Work out the cost of the water needed to fill the tank.

1 m3 = 1000 litres

5 marks
Show answer
£9.00
10

A cuboid has a square base of side 5 cm and height h cm.

The total surface area of the cuboid is 190 cm2.

Work out the volume of the cuboid.

5 marks
Show answer
175 cm³

Extension questions: beyond the core Year 9 objectives, for pupils who want a stretch.

11

The diagram shows a solid cylinder with radius 4 cm and height 10 cm.

  1. Work out the volume of the cylinder. Give your answer in terms of π.
  2. Work out the total surface area of the cylinder. Give your answer in terms of π.
  3. A sphere has radius 3 cm. Work out its volume and its surface area. Give your answers in terms of π.
    Volume of a sphere = 43πr3    Surface area of a sphere = 4πr2
4 cm10 cm
5 marks
Show answer
a) 160π cm³ b) 112π cm² c) volume 36π cm³, surface area 36π cm²
12

A cylinder has a volume of 1500 cm3 and a radius of 6 cm.

Work out the height of the cylinder.

Give your answer correct to 1 decimal place.

4 marks
Show answer
13.3 cm

Extension questions: beyond the core Year 9 objectives, for pupils who want a stretch.

13
  1. A square-based pyramid has a base of side 6 cm and a vertical height of 10 cm. Work out the volume of the pyramid.
    Volume of a pyramid = 13 × area of base × height
  2. The diagram shows a solid cone with base radius 3 cm, vertical height 4 cm and slant height 5 cm.
    Work out the volume and the total surface area of the cone. Give your answers in terms of π.
    Volume of a cone = 13πr2h    Curved surface area of a cone = πrl
4 cm3 cm5 cm
5 marks
Show answer
a) 120 cm³ b) volume 12π cm³, total surface area 24π cm²
14

A solid is made from a cone and a hemisphere.

The cone has base radius 5 cm and vertical height 9 cm.

The flat face of the hemisphere, of radius 5 cm, is joined to the base of the cone.

Work out the total volume of the solid.

Give your answer correct to 3 significant figures.

5 cm9 cmCentral vertical cross-sectionDiagram NOT accurately drawn
4 marks
Show answer
497 cm³

Your score

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Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.

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