Area of Cross-section × Length: Mixed Review
Mathematics
GCSE Higher
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A comprehensive worksheet reviewing the concept of calculating the volume of prisms using the area of cross-section multiplied by length, including procedural, reasoning, real-world, and extension questions.
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Area of Cross-section × Length: Mixed Review
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Practice Questions
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 20 cm² and a length of 15 cm.
[2 marks]2.
A triangular prism has a cross-sectional area of 12 m² and a length of 8 m. Find its volume.
[2 marks]3.
Construct a prism on the grid with a rectangular cross-section of 6 cm by 4 cm and a length of 10 cm. What is its volume?
[3 marks]4.
A cylinder has a circular cross-section with a radius of 3 m and a height of 10 m. Calculate its volume.
[3 marks]5.
Identify the error in this calculation: A prism with cross-sectional area 25 m² and length 12 m was calculated to have a volume of 250 m³. Explain the mistake.
[2 marks]6.
A compound prism consists of a rectangular block (area 18 cm², length 20 cm) and a triangular prism (area 10 cm², length 20 cm). Find the total volume.
[3 marks]7.
Plot the graph of y = 2x for x from 0 to 10. Based on the graph, estimate the volume of a prism with cross-sectional area proportional to y and length corresponding to x = 0 to 10.
[3 marks]8.
Construct a triangular prism with a base of 5 cm, height of 4 cm, and length of 12 cm. Calculate its volume.
[3 marks]9.
A real-world scenario: A swimming pool in the shape of a rectangular prism has a cross-sectional area of 50 m² and is 25 m long. What is its volume in cubic meters?
[2 marks]10.
Challenge: Find the volume of a prism with a cross-sectional area that varies linearly from 10 m² at one end to 30 m² at the other end, with a length of 20 m. Assume linear variation and provide the approximate volume.
[4 marks]11.
A prism's cross-section is a complex polygon with an area of 18 cm², but students mistakenly calculate it as 12 cm². What is the common mistake, and how would correcting it affect the volume calculation?
[2 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet