EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Cylinders and Spheres
Cylinders and spheres · Area and volume · Lesson 6 of 7 · 14 marks · 30 minutes
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Instructions
• Answer all the questions.
• Write your answers in the spaces provided.
• The marks for each question are shown in brackets - use this as a guide to how much to write.
• The answers are on separate pages at the back. Attempt every question before you look at them.
• Answer all questions. Show your working.
Question 1 CALCULATOR (2 marks)
The diagram shows a cylinder with radius 5 cm and height 12 cm. Work out the volume of the cylinder. Give your answer correct to 3 significant figures.
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(Total for Question 1 = 2 marks)
Question 2 CALCULATOR (3 marks)
Work out the total surface area of the cylinder in the last question. Give your answer correct to 3 significant figures.
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(Total for Question 2 = 3 marks)
Question 3 CALCULATOR (2 marks)
A sphere has a radius of 6 cm. Work out the volume of the sphere. Give your answer correct to 3 significant figures.
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(Total for Question 3 = 2 marks)
Question 4 CALCULATOR (2 marks)
Work out the surface area of the sphere in the last question. Give your answer correct to 3 significant figures.
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(Total for Question 4 = 2 marks)
Question 5 CALCULATOR (3 marks)
A cylinder has a volume of 200 cm³ and a radius of 4 cm. Work out the height of the cylinder. Give your answer correct to 2 decimal places.
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(Total for Question 5 = 3 marks)
Question 6 NON-CALCULATOR (2 marks)
A solid hemisphere has a radius of 3 cm. Work out the volume of the hemisphere. Give your answer in terms of π.
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(Total for Question 6 = 2 marks)
TOTAL FOR PAPER = 14 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (2 marks)
π × 5² × 12 = 300π= 942 cm³.
• π × 5² × 12 M1
• 942 A1
Question 2 (3 marks)
2π × 5² + 2π × 5 × 12 = 50π+ 120π= 170π= 534 cm².
• 2πr² M1
• 2πr h M1
• 534 A1
Question 3 (2 marks)
4/3π × 6³ = 288π= 905 cm³.
• 4/3π × 6³ M1
• 905 A1
Question 4 (2 marks)
4π × 6² = 144π= 452 cm².
• 4π × 6² M1
• 452 A1
Question 5 (3 marks)
π × 4² × h = 200, so h = 200/16π = 3.98 cm.
• π × 4² × h = 200 M1
• 200/16π M1
• 3.98 A1
Question 6 (2 marks)
⅔π × 3³ = 18π cm³.
• ⅔π × 27 or half of 4/3π × 27 M1
• 18π A1