πr² + πrl: Challenge & Extension
Mathematics
Grade 7
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the surface area formula πr² + πrl for cones, including practice, reasoning, and extension questions.
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πr² + πrl: Challenge & Extension
Subject: MathematicsGrade: Grade 7
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Untitled Worksheet
Grade Grade 7
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 using the formula πr² + πrl. Use π ≈ 3.14.
[3 marks]2.
If the radius of a cone is doubled to 6 cm and the slant height remains 5 cm, what is the new surface area? Show your working.
[4 marks]3.
A cone has a radius of 4 cm and a slant height of 6 cm. Calculate its surface area.
[3 marks]4.
Explain why increasing the slant height of a cone while keeping the radius constant increases its surface area.
[2 marks]5.
A cone has a surface area of 150 cm², with a radius of 5 cm. Find the slant height.
[4 marks]6.
Construct a cone on the grid with a radius of 2 cm and a slant height of 4 cm. Label the radius and slant height in your drawing.
[2 marks]7.
Calculate the surface area of a cone with radius 7 cm and slant height 10 cm. Use π ≈ 3.14.
[3 marks]8.
A cone has a radius of 3 cm and a surface area of 94.2 cm². What is its slant height? Show your working.
[4 marks]9.
A real-world scenario: A traffic cone has a radius of 0.2 meters and a slant height of 0.5 meters. Calculate its surface area and suggest why understanding this might be important for safety markings.
[3 marks]10.
Identify and correct the mistake in this calculation: A cone with radius 4 cm and slant height 6 cm has surface area 150 cm², but the calculation used πr² + 2πrl.
[2 marks]11.
Challenge: Derive the formula for the surface area of a cone starting from the lateral area formula and the area of the base.
[3 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet