Sphere: Error Analysis & Misconceptions
Mathematics
GCSE Higher
14 questions
~28 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on common misconceptions and error analysis related to spheres, designed for GCSE Higher students to develop procedural mastery and reasoning skills.
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Sphere: Error Analysis & Misconceptions
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Introduction
Read the key concepts about spheres. Recall that the surface area of a sphere is given by 4πr² and the volume by (4/3)πr³. Be attentive to common errors in applying these formulas.
B
Fluency & Practice
Answer the following questions to practice calculating surface area and volume of spheres.
1.
Calculate the surface area of a sphere with a radius of 5 cm.
[3 marks]2.
Find the volume of a sphere with a radius of 3 meters.
[3 marks]3.
A sphere has a surface area of 1256.64 cm². What is its radius?
[4 marks]4.
Calculate the volume of a sphere with radius 7 cm.
[3 marks]C
Problem Solving & Reasoning
Answer the following multi-step questions that involve reasoning about spheres and their properties.
1.
A spherical ball has a diameter of 12 cm. If a smaller sphere with radius 3 cm is cut out from its center, what is the volume of the remaining hollow spherical region?
[6 marks]2.
Explain why calculating the surface area by only using the radius without considering the sphere's actual surface can lead to errors.
[4 marks]3.
A sphere's surface area is mistakenly calculated as 600 cm² when the radius is 6 cm. Identify and correct the mistake.
[4 marks]D
Real-world Applications
Solve the following context-based problems involving spheres.
1.
A globe has a radius of 15 cm. How much paper is needed to cover its surface? Use π ≈ 3.14.
[3 marks]2.
A spherical tank with a radius of 8 meters is to be painted outside. How much area will need painting?
[3 marks]E
Challenge & Extension
Attempt the following more advanced questions to deepen your understanding of spheres.
1.
A sphere with radius r has a surface area of 1008 cm². Derive an expression for r in terms of the surface area, and calculate r.
[6 marks]2.
If the radius of a sphere is increased by 50%, by what percentage does its volume increase?
[4 marks]F
Mixed Review & Error Analysis
Identify and correct the errors in the following statements or calculations about spheres.
1.
A student claims that the surface area of a sphere with radius 10 cm is 400π cm². Is this correct? If not, correct the mistake.
[4 marks]2.
A formula for the volume of a sphere is written as V = 3πr³. Identify the error and provide the correct formula.
[4 marks]3.
A sphere's radius is 4 cm, but a student mistakenly calculates the surface area as 4π(4) = 16π cm². Explain and correct the mistake.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet