Cuboids: Challenge & Extension
Mathematics
Grade 6
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet exploring Pythagoras in 3D within cuboids, including procedural practice, problem solving, real-world applications, and extension challenges.
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Cuboids: Challenge & Extension
Subject: MathematicsGrade: Grade 6
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Untitled Worksheet
Grade Grade 6
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the space diagonal of a cuboid measuring 6 cm by 8 cm by 10 cm.
[2 marks]2.
Find the length of the diagonal across the face measuring 5 cm by 12 cm.
[2 marks]3.
A cuboid has length 9 cm, width 4 cm, and height 12 cm. What is the space diagonal?
[3 marks]4.
Construct a cuboid with dimensions 3 cm by 4 cm by 5 cm and draw its space diagonal.
[3 marks]B
Problem Solving & Reasoning
Answer all questions. Provide explanations for your solutions.
1.
A rectangular box has dimensions of 7 cm, 24 cm, and 25 cm. Determine the length of the space diagonal. Explain your steps.
[4 marks]2.
A cuboid's length is twice its width, and its height is 3 times its width. If the space diagonal is 15 cm, find the dimensions of the cuboid.
[5 marks]C
Real-world Applications
Answer all questions. Use the grid for calculations where appropriate.
1.
A storage box measures 2 m by 1.5 m by 1 m. Calculate the length of the longest straight line you could run from one corner of the box to the opposite corner inside.
[3 marks]2.
A shipping crate has dimensions 1.2 m by 0.8 m by 0.6 m. Find the internal diagonal distance to the nearest centimeter.
[3 marks]D
Challenge & Extension
Attempt these advanced problems. Show full working for each.
1.
Design a cuboid with a volume of 216 cm³, where the length is twice the width, and the height is 3 cm more than the width. Calculate its space diagonal.
[4 marks]2.
A cube has a side length of 9 cm. Calculate the length of its space diagonal and compare it to the face diagonal. Show your reasoning.
[3 marks]E
Mixed Review & Error Analysis
Answer the questions below and identify common mistakes if applicable.
1.
A student calculates the space diagonal of a cuboid with dimensions 3 cm, 4 cm, and 5 cm as 7 cm. Explain what mistake they made and correct it.
[3 marks]2.
A student finds the face diagonal as 13 cm for a rectangle 5 cm by 12 cm, then claims this is the space diagonal of the cuboid. Identify the error.
[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)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet