General 3D Shapes: Challenge & Extension
Mathematics
GCSE Foundation
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A worksheet exploring Pythagoras' theorem applied to 3D shapes, including calculations and real-world contexts for GCSE Foundation students.
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General 3D Shapes: Challenge & Extension
Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet
Grade GCSE Foundation
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the length of the diagonal of a cuboid with sides 3 cm, 4 cm, and 12 cm.
[3 marks]2.
Find the space diagonal of a cube with side length 5 cm.
[2 marks]3.
A rectangular prism has length 8 cm, width 6 cm, and height 10 cm. Calculate the space diagonal.
[3 marks]4.
Construct a right-angled triangle with legs 6 cm and 8 cm on the grid. Find the hypotenuse.
[2 marks]B
Problem Solving & Reasoning
Answer all questions. Show detailed working.
1.
A ladder leans against a wall, forming a right-angled triangle with the ground and the wall. If the ladder is 10 m long and the base is 6 m from the wall, find the height the ladder reaches on the wall.
[4 marks]2.
A rectangular box has a length of 4 cm, a width of 3 cm, and a height of 12 cm. Calculate the length of the space diagonal. Explain your reasoning.
[4 marks]3.
A cube has a volume of 125 cm³. Find the length of its space diagonal and justify your answer.
[3 marks]C
Real-world Applications
Answer all questions. Show your working and reasoning.
1.
A builder needs to determine the length of a steel rod that will span from the top corner of a rectangular building (height 15 m, length 20 m) to a point directly opposite at ground level. Calculate the length of the rod, assuming it runs diagonally across the interior space.
[4 marks]2.
A storage container is shaped like a rectangular prism with dimensions 2 m, 3 m, and 4 m. A safety inspection requires checking the longest internal diagonal. Calculate this length.
[3 marks]D
Challenge & Extension
Answer all questions. These are more advanced problems requiring multi-step reasoning.
1.
A rectangular prism has dimensions 5 cm by 12 cm by 13 cm. Calculate the length of the space diagonal using Pythagoras' theorem in 3D. Show all steps.
[4 marks]2.
A cube has a surface area of 150 cm². Calculate the length of the space diagonal. Provide detailed working and reasoning.
[4 marks]E
Mixed Review & Error Analysis
Attempt all questions. For errors, identify and correct the mistake in the calculation.
1.
A rectangular box with sides 4 cm, 7 cm, and 9 cm is said to have a space diagonal of 12 cm. Identify the mistake and calculate the correct length of the diagonal.
[2 marks]2.
A student incorrectly calculates the diagonal of a cube with side 6 cm as 36 cm. Explain the mistake and find the correct diagonal length.
[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.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet