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Volume of 3D Shapes

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Volume of 3D Shapes

A community workshop is planning storage and water systems for a pop-up gear shed. Solve each problem, show your working, and include units. Use π = 3.14 unless a question says otherwise. Give answers to 2 decimal places where needed.

Choose the right model

Use the formula bank to answer Questions 1–3: cuboid: V = lwh; cube: V = s³; cylinder: cylinder volume is found using its radius and height; triangular prism: V = (½ × base × triangle height) × prism length.

1.The shed’s water container is a cylinder. Which formula would you use to find its volume?

V = lwh
V = s³
V = πr²h
V = ½ × base × height

2.A crate is 1.2 m long, 0.8 m wide and 0.6 m high. Calculate its volume in cubic metres.

3.A cube-shaped stool has edges of 0.45 m. Find its volume in cubic metres.

4.A rainwater drum has radius 0.35 m and height 1.1 m. Calculate its volume in cubic metres, to 2 decimal places.

Plan and compare

The workshop is choosing practical storage solutions. Remember that 1 m³ = 1,000,000 cm³ and 1 m³ = 1,000 L.

5.A toolbox measures 60 cm × 35 cm × 28 cm. Find its volume in cm³, then convert it to litres.

6.Two water tanks are being compared. Tank A is cylindrical with radius 0.5 m and height 1.6 m. Tank B is a cuboid measuring 1 m × 0.8 m × 1.2 m. Which tank holds more, and by how many cubic metres?

7.A triangular-prism display stand has a triangular cross-section with base 0.8 m and perpendicular height 0.6 m. The prism is 1.5 m long. Calculate its volume.

8.A cylindrical post with radius 0.1 m passes vertically through a solid concrete block measuring 1.2 m × 0.8 m × 0.5 m. The hole goes through the full 0.5 m height. Find the volume of concrete remaining.

Explain the scale-up

Use the cube’s dimensions to reason about how volume changes when every length changes by the same scale factor.

9.A cube-shaped storage module has side length 0.4 m. A second version doubles every edge to 0.8 m. Calculate both volumes and explain how many times larger the second volume is.

10.A tank’s volume is 2.4 m³. It is filled to 75% of its capacity. How many litres of water are in it?

11.A rectangular storage bay has a fixed volume of 3.6 m³. Its base is 1.5 m long and 1.2 m wide. How high is the bay? Show how you rearranged the volume formula.