2πr² + 2πrh: Challenge & Extension
Mathematics
Grade 8
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A challenging worksheet focusing on the surface area of cylinders, specifically the formula 2πr² + 2πrh, designed to extend students' understanding through varied problem types.
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2πr² + 2πrh: Challenge & Extension
Subject: MathematicsGrade: Grade 8
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Date:
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Untitled Worksheet
Grade Grade 8
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the surface area of a cylinder with radius 4 cm and height 10 cm using the formula 2πr² + 2πrh.
[3 marks]2.
Find the lateral surface area of a cylinder with radius 3.5 m and height 8 m.
[2 marks]3.
A cylinder has a surface area of 150π square units and a radius of 5 units. Find its height.
[3 marks]B
Problem Solving & Reasoning
Answer all questions. Provide detailed explanations where necessary.
1.
A cylindrical water tank has a radius of 2.5 meters and a height of 4 meters. If the tank's surface area increases by 50% due to an added coating, what is the new surface area? Show your working.
[4 marks]2.
Explain why increasing the radius of a cylinder has a greater effect on surface area than increasing the height, assuming both are increased by the same amount.
[3 marks]C
Real-world Applications
Answer all questions. Use calculations to support your answers.
1.
A manufacturer produces cylindrical cans with radius 3 cm and height 10 cm. If a coating is applied evenly on the entire surface, what is the total area covered? How much more area is covered compared to a cylindrical container with radius 2.5 cm and height 10 cm?
[4 marks]D
Challenge & Extension
Answer all questions. These are more complex problems designed to extend your understanding.
1.
Given a cylinder with surface area 200π cm², find all possible integer values of radius and height if the radius is less than 10 cm.
[4 marks]2.
Design a cylinder with a surface area of 300π square units that maximizes volume. State your dimensions and explain your reasoning.
[4 marks]E
Mixed Review
Answer all questions. Mix of different question types to review surface area concepts.
1.
Construct a cylinder on the grid with radius 6 units and height 15 units. Label the dimensions.
[2 marks]2.
Plot the graph of y=2x on the grid, then calculate the surface area of a cylinder with radius x = 4 units and height y = 8 units.
[2 marks]3.
Identify the common mistake: a student calculates the surface area as 2πr² + 2πh without multiplying 2π by the radius in the lateral surface area formula. Explain and correct the mistake.
[3 marks]F
Error Analysis
Review the following common mistake and correct it.
1.
A student computes the surface area of a cylinder with radius 3 cm and height 7 cm as 2π(3)² + 2π(7). Identify the mistake and provide the correct calculation.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet