⅓πr²h: Challenge & Extension
Mathematics
GCSE Higher
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the volume of cones using the formula ⅓πr²h, designed to challenge higher-tier GCSE students with a variety of problem types.
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⅓πr²h: Challenge & Extension
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the volume of a cone with radius 4 cm and height 9 cm using ⅓πr²h.
[2 marks]2.
A cone has a radius of 6 cm and a height of 12 cm. Find its volume, giving your answer in cubic centimeters rounded to one decimal place.
[3 marks]3.
If the volume of a cone is 314.16 cm³ and the height is 10 cm, what is the radius of the cone? (Use 3 decimal places for your answer).
[3 marks]4.
Construct a cone on the grid with a radius of 3 cm and a height of 7 cm. Calculate its volume using the formula.
[3 marks]5.
Plot the graph of y = ⅓πr²h for a fixed height of 10 cm as the radius r varies from 1 cm to 10 cm. (Draw on the grid.)
[2 marks]6.
A conical tank has a radius of 5 meters and a height of 8 meters. Calculate the volume of water it can hold.
[3 marks]7.
A cone is made by rotating a right triangle with a base of 4 cm and height of 9 cm. Find the volume of the cone.
[2 marks]8.
Determine the height of a cone with radius 3 cm if its volume is 42.4 cm³.
[3 marks]9.
An engineer is designing a conical funnel. If the volume of the cone is 500 cm³ and the radius at the opening is 5 cm, what is the height of the funnel? (Round to two decimal places.)
[3 marks]10.
Identify and correct the common mistake in calculating the volume of a cone if a student uses πr²h without multiplying by ⅓.
[2 marks]11.
Challenge: A conical pile of sand has a height of 4 meters and a radius of 3 meters. If a new pile is built with a height of 6 meters, assuming the same shape, what is its approximate volume? (Show your working.)
[4 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet