⁴⁄₃πr³: Error Analysis & Misconceptions

Mathematics
Grade 8
12 questions
~24 mins
1 views0 downloads

About This Worksheet

A worksheet focused on understanding, calculating, and correcting misconceptions related to the volume of spheres using the formula ⁴⁄₃πr³ for Grade 8 students.

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⁴⁄₃πr³: Error Analysis & Misconceptions

Subject: MathematicsGrade: Grade 8
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Untitled Worksheet

Grade Grade 8
A

Fluency & Practice

Calculate the volume of each sphere. Show your working in the grid spaces provided.
1.
A sphere has a radius of 3 cm. Calculate its volume using ⁴⁄₃πr³.
[2 marks]
2.
A sphere with radius 5 inches. Find its volume, rounding to two decimal places.
[2 marks]
3.
Calculate the volume of a sphere with a radius of 2.5 meters.
[2 marks]
4.
Find the volume of a sphere with radius 7 cm.
[2 marks]
B

Problem Solving & Reasoning

Answer the following multi-step problems, explaining your reasoning.
1.
A tennis ball has a radius of 3.8 cm. Calculate its volume. Then, determine how many such tennis balls are needed to fill a container with a volume of 2 liters.
[4 marks]
2.
A spherical water tank has a radius of 10 meters. If the tank is only 75% full, what is the volume of the water inside?
[4 marks]
C

Real-world Applications

Solve these contextual word problems related to spheres and their volume.
1.
A spherical planet has a radius of 6,371 km. Calculate its approximate volume in cubic kilometers.
[3 marks]
2.
A glass ornament in the shape of a sphere has a radius of 4 cm. If it is filled with a liquid that occupies 80% of its volume, what is the volume of the liquid?
[3 marks]
D

Challenge & Extension

Tackle these advanced problems involving the volume of spheres and related concepts.
1.
A sphere's volume is calculated as ⁴⁄₃πr³. If the volume is 904.78 cubic units, find the radius of the sphere.
[3 marks]
2.
Prove that the ratio of the volumes of two spheres is proportional to the cube of the ratio of their radii.
[4 marks]
E

Mixed Review & Error Analysis

Review and correct the following common mistakes in volume calculations.
1.
A student calculates the volume of a sphere with radius 4 cm as V = 4/3 * π * 4.3. Identify the mistake and provide the correct calculation.
[3 marks]
2.
A student forgets to cube the radius when calculating the volume. They compute volume as ⁴⁄₃π * 5 = 52.36. Explain and correct the mistake.
[3 marks]

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Details

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