EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Pyramids and Cones
Pyramids and cones · Area and volume · Lesson 7 of 7 · 15 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 NON-CALCULATOR (2 marks)
A square-based pyramid has a base of side 6 cm and a perpendicular height of 9 cm. Work out the volume of the pyramid.
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(Total for Question 1 = 2 marks)
Question 2 CALCULATOR (2 marks)
A cone has a base radius of 4 cm and a perpendicular height of 9 cm. Work out the volume of the cone. Give your answer correct to 3 significant figures.
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(Total for Question 2 = 2 marks)
Question 3 NON-CALCULATOR (3 marks)
The diagram shows a cone with base radius 5 cm and vertical height 12 cm. Work out the curved surface area of the cone. Give your answer in terms of π.
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(Total for Question 3 = 3 marks)
Question 4 CALCULATOR (2 marks)
Work out the volume of the cone 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 (4 marks)
A cone has base radius 6 cm and height 12 cm. A smaller cone of base radius 3 cm and height 6 cm is cut off the top, leaving a frustum. Work out the volume of the frustum. Give your answer correct to 3 significant figures.
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(Total for Question 5 = 4 marks)
Question 6 NON-CALCULATOR (2 marks)
A pyramid has a rectangular base measuring 8 cm by 6 cm and a perpendicular height of 5 cm. Work out the volume of the pyramid.
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(Total for Question 6 = 2 marks)
TOTAL FOR PAPER = 15 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (2 marks)
⅓ × 36 × 9 = 108 cm³.
• ⅓ × 6 × 6 × 9 M1
• 108 A1
Question 2 (2 marks)
⅓π × 4² × 9 = 48π= 151 cm³.
• ⅓π × 4² × 9 M1
• 151 A1
Question 3 (3 marks)
The slant height is √(5² + 12²) = 13 cm. The curved surface area is π × 5 × 13 = 65π cm².
• 5² + 12² M1
• Slant height 13 A1
• 65π A1
Question 4 (2 marks)
⅓π × 5² × 12 = 100π= 314 cm³.
• ⅓π × 5² × 12 M1
• 314 A1
Question 5 (4 marks)
Large cone: ⅓π × 6² × 12 = 144π. Small cone: ⅓π × 3² × 6 = 18π. Frustum: 126π= 396 cm³.
• Volume of the large cone M1
• Volume of the small cone M1
• Subtracting M1
• 396 A1
Question 6 (2 marks)
⅓ × 8 × 6 × 5 = 80 cm³.
• ⅓ × 8 × 6 × 5 M1
• 80 A1