⅓ × Base Area × Height: Real-world Applications
Mathematics
GCSE Higher
16 questions
~32 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on the volume formula for pyramids, emphasizing real-world science experiment contexts.
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⅓ × Base Area × Height: Real-world Applications
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the volume of a pyramid with a base area of 50 cm² and a height of 12 cm.
[2 marks]2.
A pyramid has a base area of 80 m² and a height of 15 m. Find its volume.
[2 marks]3.
Describe the effect on volume if the base area doubles but the height remains the same.
[3 marks]4.
Construct a pyramid with a base area of 40 cm² and a height of 10 cm. Calculate its volume.
[2 marks]B
Problem Solving & Reasoning
Answer all questions. Show detailed working.
1.
A science experiment involves creating a pyramid-shaped container with a base area of 60 cm² and a height of 20 cm. What is its volume? How could changing the height affect the amount of liquid it can hold?
[4 marks]2.
A pyramid with a base length of 10 m and a height of 18 m has a square base. Calculate its volume.
[3 marks]3.
In a series of experiments, students vary the height while keeping the base area fixed at 25 cm². Explain how the volume changes as height increases.
[3 marks]C
Real-world Applications
Answer all questions. Use calculations to support your answers.
1.
A glass sculpture in the shape of a pyramid has a base area of 150 cm² and a height of 25 cm. Calculate the volume of the sculpture.
[3 marks]2.
A scientist designs a pyramid-shaped tank with a base area of 80 m² and a height of 10 m. How much liquid can it hold?
[3 marks]3.
If the height of the pyramid in a science experiment is halved, what happens to its volume?
[2 marks]D
Challenge & Extension
Answer these advanced questions. Show detailed working.
1.
Design a pyramid with a base area of 100 cm² and a height such that its volume is exactly 500 cm³. Find the height.
[3 marks]2.
A pyramid's volume is calculated incorrectly by using the formula Volume = Base Area × Height without multiplying by ⅓. What is the percentage error introduced?
[3 marks]E
Mixed Review
Answer all questions. Mix of question types for variety.
1.
Calculate the volume of a pyramid with base area 45 cm² and height 9 cm.
[2 marks]2.
Construct a pyramid on your grid paper with a base area of 20 cm² and height of 8 cm. Find the volume.
[3 marks]F
Error Analysis
Identify common mistakes and suggest corrections.
1.
A student calculates the volume of a pyramid as 300 cm³ when the base area is 50 cm² and the height is 15 cm, using the formula Volume = Base Area × Height. Identify and explain the mistake.
[3 marks]2.
A student doubles the base area and keeps the height the same, then calculates the volume. Is the calculation correct? Why or why not?
[2 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