12 original questions, 42 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.
Diagram a shows the net of a 3D solid. Write down the name of the solid.
Diagram b shows part of the net of a cuboid that measures 3 cm by 2 cm by 1 cm, drawn on a centimetre grid. Two faces are missing. On the grid, draw the two missing faces to complete the net.
3 marks
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a) triangular prism b) a 1 cm by 2 cm rectangle on the right of the 3 by 2 face, and a 3 cm by 2 cm rectangle above the top 3 by 1 face
2
A cuboid measures 5 cm by 3 cm by 2 cm.
Work out the total surface area of the cuboid.
State the units of your answer.
3 marks
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62 cm²
3
The cross-section of a prism is a trapezium.
The parallel sides of the trapezium are 6 cm and 10 cm, and the perpendicular distance between them is 4 cm.
The length of the prism is 15 cm.
Work out the volume of the prism.
3 marks
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480 cm³
4
A cylinder has a radius of 5 cm and a height of 12 cm.
Work out the volume of the cylinder.
Give your answer correct to 3 significant figures.
3 marks
Show answer
942 cm³
5
A garden pond is a cuboid 2.5 m long, 1.2 m wide and 0.6 m deep.
The pond is filled with water from a hose. Water flows from the hose at 15 litres per minute.
Work out how long it takes to fill the pond. Give your answer in hours.
1 m3 = 1000 litres
3 marks
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2 hours
6
The diagram shows a triangular prism. The cross-section is a right-angled triangle with sides 6 cm, 8 cm and 10 cm. The prism is 15 cm long.
Work out the volume of the prism.
Work out the total surface area of the prism.
4 marks
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a) 360 cm³b) 408 cm²
7
A tin of beans is a closed cylinder with radius 4 cm and height 11 cm.
A paper label covers the curved surface of the tin. Work out the area of the label.
Work out the total surface area of the tin.
Give your answers correct to 1 decimal place.
4 marks
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a) 276.5 cm²b) 377.0 cm²
8
A cylindrical water butt has a radius of 25 cm and a height of 80 cm.
Work out the number of litres of water the water butt holds when it is full.
Give your answer to the nearest litre.
1 litre = 1000 cm3
4 marks
Show answer
157 litres
9
A cube has a total surface area of 150 cm2.
Show that the volume of the cube is 125 cm3.
4 marks
Show answer
Face area = 150 ÷ 6 = 25 cm², so side = 5 cm and volume = 5³ = 125 cm³
10
A skate ramp is made of concrete. It is a triangular prism. The cross-section is a right-angled triangle with base 3 m and height 1.2 m. The ramp is 2.5 m wide.
Concrete costs £95 per m3.
Work out the cost of the concrete for the ramp.
3 marks
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£427.50
11
A closed wooden box is a cuboid measuring 40 cm by 25 cm by 20 cm.
Amira varnishes all 6 faces of each box.
One tin of varnish covers 5000 cm2.
Amira has 3 tins of varnish.
Work out the greatest number of boxes Amira can varnish completely.
4 marks
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3
12
A hall has 8 cylindrical pillars.
Each pillar has a radius of 0.25 m and a height of 3 m.
Ben paints the curved surface of every pillar.
One tin of paint covers 8 m2.
Work out the number of tins of paint Ben must buy.
4 marks
Show answer
5
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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.