General 3D Shapes: Real-world Applications
Mathematics
GCSE Foundation
15 questions
~30 mins
1 views0 downloads
About This Worksheet
A worksheet covering Pythagoras in 3D applied to general 3D shapes for GCSE Foundation students. This worksheet includes procedural questions, real-world problems, and extension challenges.
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General 3D Shapes: Real-world Applications
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 space diagonal of a cuboid measuring 3 cm by 4 cm by 12 cm.
[2 marks]2.
A right-angled triangle has legs of 5 cm and 12 cm. Find the hypotenuse.
[2 marks]3.
Construct a rectangular prism with length 6 cm, width 8 cm, and height 10 cm. Calculate its space diagonal.
[3 marks]4.
In a cube, each edge measures 5 cm. Find the length of the space diagonal.
[2 marks]B
Problem Solving & Reasoning
Answer all questions, showing detailed working where appropriate.
1.
A ladder leans against a wall, reaching a height of 8 meters. The distance from the wall to the base of the ladder is 6 meters. Calculate the length of the ladder.
[3 marks]2.
A rectangular box has dimensions 4 cm, 3 cm, and 12 cm. Find the length of the space diagonal and justify your answer.
[4 marks]3.
Explain why the Pythagoras theorem is applicable when calculating the space diagonal of a rectangular prism.
[3 marks]C
Real-world Applications
Answer the following context-based questions.
1.
A designer is creating a box for shipping. The box measures 30 cm by 20 cm by 10 cm. What is the length of the longest possible straight line inside the box?
[3 marks]2.
A piece of pipe is to be cut to fit diagonally through a cuboid-shaped tank measuring 8 m x 6 m x 4 m. Calculate the pipe length needed.
[3 marks]3.
A construction worker measures a rectangular prism with dimensions 5 m, 12 m, and 13 m. They need to install a support rod from one corner to the opposite top corner. How long is the support rod?
[3 marks]D
Challenge & Extension
Attempt these advanced problems for extra challenge.
1.
A cube has a volume of 125 cm³. Calculate the length of its space diagonal.
[3 marks]2.
A rectangular prism has a length of 9 cm, width of 12 cm, and height of 15 cm. Find the length of its space diagonal, and verify your answer by rounding to two decimal places.
[4 marks]E
Mixed Review
Answer these varied questions to consolidate your understanding.
1.
Construct a rectangular prism with edges 7 cm, 24 cm, and 25 cm. Calculate its space diagonal.
[3 marks]2.
A cuboid has edges of 6 cm, 8 cm, and 10 cm. Find the length of the space diagonal.
[2 marks]F
Error Analysis
Identify and correct the common mistake in the following question.
1.
A student calculates the space diagonal of a cube with edge 4 cm as 8 cm, using the formula diagonal = 2 × 4. Identify the mistake and correct it.
[3 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)
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet