πr² + πrl: Problem Solving & Reasoning
Mathematics
GCSE Higher
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on calculating the surface area of cones using the formula πr² + πrl, including procedural, contextual, and extension questions for GCSE Higher students.
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πr² + πrl: Problem Solving & Reasoning
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 surface area of a cone with a radius of 3 cm and a slant height of 5 cm. Use the formula πr² + πrl.
[2 marks]2.
A cone has a radius of 4 cm and a slant height of 6 cm. Find its surface area.
[2 marks]3.
A cone with radius 2.5 cm has a lateral surface area of 39.25 cm². Find the slant height l.
[3 marks]4.
Construct a cone on the grid with a radius of 3 cm and a slant height of 5 cm. Show the key points and outline the surface area calculation.
[4 marks]5.
A conical cup has a radius of 4.5 cm and a height of 9 cm. Determine its total surface area, given the slant height is approximately 10.1 cm.
[4 marks]6.
A cone's total surface area is 150 cm². If the radius is 3 cm, find the slant height l.
[3 marks]7.
A cone with radius 2 cm has a lateral surface area of 12.56 cm². Find the slant height l.
[2 marks]8.
Explain why a miscalculation of πr² + πrl can lead to an overestimation of the surface area of a cone. Provide an example with specific numbers.
[4 marks]9.
Calculate the lateral surface area of a cone with radius 5 cm and slant height 8 cm.
[2 marks]10.
A factory produces conical storage tanks with a radius of 6 m and a slant height of 10 m. Calculate the total surface area for one tank.
[4 marks]11.
Identify and correct the mistake in the following calculation: A cone with radius 3 cm and slant height 4 cm is said to have surface area 50.27 cm². (Correct calculation: π(3)² + π(3)(4) = approximately 50.27 cm².)
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet