Year 10 area test to download as PDF

This Year 10 area test lasts 45 minutes and is marked out of 20. It covers the whole chapter for pupils aged 14-15, and the full answers are on a separate page.

⏱️ Duration : 45 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Areas and circles
Calculator allowed. Give answers to 1 decimal place where needed.
1. A trapezium has parallel sides 8 cm and 14 cm and height 6 cm. Work out its area. (2 marks)
2. Work out the circumference and area of a circle with radius 7 cm. (2 marks)
Question 2 – Prisms
A triangular prism has a right-angled triangle for its cross-section, with perpendicular sides 6 cm and 8 cm and hypotenuse 10 cm. The prism is 15 cm long.
1. Work out the volume. (2 marks)
2. Work out the total surface area. (2 marks)
Question 3 – Arcs and sectors
A sector of a circle has radius 9 cm and angle \(120^\circ\). Calculator allowed.
1. Work out the arc length, giving your answer in terms of \(\pi\) and to 1 d.p. (2 marks)
2. Work out the area of the sector to 1 d.p. (2 marks)
Question 4 – Problem: the oil tank
A cylindrical oil tank has diameter 1.2 m and length 2 m. It lies on a stand. Heating oil costs 68p per litre.
1. Show that the tank holds about 2262 litres when full. (2 marks)
2. Work out the cost of filling the tank completely, to the nearest £. (2 marks)
Question 5 – Higher: cone and sphere
Higher tier. A cone has base radius 6 cm and vertical height 8 cm. A sphere has radius 3 cm.
1. Work out the slant height of the cone. (1 mark)
2. Work out the volume of the cone in terms of \(\pi\). (1 mark)
3. Work out the volume of the sphere in terms of \(\pi\). (1 mark)
4. Find the ratio of the volume of the cone to the volume of the sphere in its simplest form. (1 mark)

How to use this Year 10 area test

First, revise with the area, volume, surface area, arcs and sectors lesson and the worksheet. Then sit the test in one go, with a timer set to 45 minutes. After that, mark your work with the area, volume, surface area, arcs and sectors test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 10 area test as a PDF and print it like a real exam paper. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.

Area, volume, surface area, arcs and sectors – Year 10 GCSE maths test to download as PDF

Question 1 – Areas and circles

Question 2 – Prisms

Question 3 – Arcs and sectors

Question 4 – Problem: the oil tank

Question 5 – Higher: cone and sphere

How to use this Year 10 area test

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