Area of Cross-section × Length: Error Analysis & Misconceptions
Mathematics
Grade 8
14 questions
~28 mins
1 views0 downloads
About This Worksheet
This worksheet explores common errors and misconceptions related to calculating the volume of prisms using the formula: Volume = Cross-sectional Area × Length. It includes practice, problem-solving, real-world applications, and extension questions.
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Area of Cross-section × Length: Error Analysis & Misconceptions
Subject: MathematicsGrade: Grade 8
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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 volume of a rectangular prism with a cross-sectional area of 24 cm² and a length of 15 cm.
[2 marks]2.
A triangular cross-section has an area of 12 cm². If the prism's length is 10 cm, what is its volume?
[2 marks]3.
Construct a rectangle with an area of 20 cm² and a length of 5 cm. Write the possible dimensions.
[2 marks]4.
Calculate the volume of a prism with a cross-sectional area of 30 cm² and a length of 8 cm.
[2 marks]B
Problem Solving & Reasoning
Answer all questions clearly, explaining your reasoning where necessary.
1.
A prism has a rectangular cross-section with length 12 cm, width 5 cm, and height 4 cm. If the length of the prism is doubled, what is the new volume? Explain your calculations.
[3 marks]2.
A student calculates the volume of a prism as 150 cm³ by multiplying the cross-sectional area 25 cm² by 6 cm. Identify and correct any mistake if the actual length is 5 cm.
[3 marks]3.
A triangular cross-section has an area of 8 cm². If the prism's volume is calculated as 48 cm³, what is the length? Show your work.
[2 marks]C
Real-world Applications
Solve the following word problems based on real-world contexts.
1.
A water tank is in the shape of a rectangular prism with a cross-sectional area of 50 m² and a length of 4 meters. How much water (in cubic meters) can the tank hold when full?
[3 marks]2.
A factory produces cylindrical rods with a cross-sectional area of 7.5 cm² and a length of 20 cm. Calculate the volume of one rod.
[2 marks]D
Challenge & Extension
Attempt these more advanced problems to extend your understanding.
1.
A prism's cross-sectional area varies linearly from 10 cm² to 50 cm² over its length of 25 cm. Find the average cross-sectional area and estimate the volume.
[3 marks]2.
Design a problem where a prism's cross-section is composed of two shapes, and explain how to compute its volume correctly.
[3 marks]E
Mixed Review & Error Analysis
Review the questions below to test your understanding and identify errors.
1.
A prism with a cross-sectional area of 18 cm² has a length of 0 cm. What is the volume? Identify the mistake if any.
[2 marks]2.
A student calculates the volume of a prism as 250 cm³ with cross-sectional area 50 cm² and length 4 cm. Is this correct? If not, fix the calculation.
[3 marks]3.
Construct a scenario where a student confuses surface area with volume. Describe how this mistake affects their volume calculation.
[3 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet