2πr² + 2πrh: Error Analysis & Misconceptions

Mathematics
GCSE Foundation
11 questions
~22 mins
1 views0 downloads

About This Worksheet

A worksheet focusing on understanding and correctly applying the surface area formula for cylinders: 2πr² + 2πrh, including common misconceptions and error analysis.

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2πr² + 2πrh: Error Analysis & Misconceptions

Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet

Grade GCSE Foundation
A

Fluency & Practice

Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the surface area of a cylinder with radius 3 cm and height 10 cm using the formula 2πr² + 2πrh.
[3 marks]
2.
A cylinder has a radius of 4 meters. If its surface area is 150.8 m², what is its height? Show your working.
[4 marks]
3.
Construct a cylinder on the grid with a radius of 2 units and height of 5 units. Calculate its surface area.
[3 marks]
B

Problem Solving & Reasoning

Answer all questions. Explain your reasoning clearly.
1.
A cylindrical tank has a radius of 5 meters and a height of 12 meters. A worker claims that reducing the radius to 4 meters will reduce the surface area by exactly 20 m². Is this statement correct? Show your calculations and reasoning.
[5 marks]
2.
Explain why a common mistake when calculating the surface area is to forget the height component in the 2πrh term. How does this affect the final answer?
[3 marks]
C

Real-world Applications

Answer all questions. Use calculations to support your answers.
1.
A water storage tank in the shape of a cylinder has a radius of 2.5 meters and height of 8 meters. Calculate its surface area to determine the amount of material needed to cover it.
[4 marks]
D

Challenge & Extension

Answer all questions. Show detailed working.
1.
A cylinder with radius r and height h has a surface area of 200π cm². If the height is doubled, what is the new surface area? Derive your answer using algebra.
[5 marks]
2.
Given a cylinder with surface area 300 cm², find possible dimensions if the radius is between 3 cm and 6 cm. Explain your reasoning.
[5 marks]
E

Mixed Review & Error Analysis

Answer all questions. Pay attention to common errors in calculations.
1.
A student calculates the surface area of a cylinder with radius 4 cm and height 10 cm as 200 cm², forgetting to include the 2πrh term. Identify the mistake and provide the correct surface area.
[3 marks]
2.
A common misconception is to treat the surface area formula as just 2πr(r+h). Why is this incorrect? Correct the formula and explain.
[4 marks]
3.
Plot a rectangle on the grid representing the lateral surface when unrolled for a cylinder with radius 3 units and height 7 units. Label the dimensions and calculate its area.
[3 marks]

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Details

Created
1/1/2026
Updated
1/1/2026
Type
worksheet