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Volume and Composite Shapes

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Volume and Composite Shapes

A community event needs sturdy storage and a small display stand. Work out the volume of each design. Show calculations and include cubic units in your answers. Use the appropriate prism formula; for a triangular prism, volume = area of triangular end × prism length, and triangle area = base × perpendicular height ÷ 2.

Part A — Build the basics

Calculate volumes carefully. Keep units consistent.

1.The event team packs signs in a rectangular-prism crate measuring 8 cm long, 5 cm wide and 3 cm high. What is the crate’s volume?

2.A display plinth is 1.2 m long, 0.5 m wide and 0.4 m high. Calculate its volume in cubic metres.

3.A triangular-prism sign weight has a triangular end with base 6 cm and perpendicular height 4 cm. The prism is 10 cm long. Find its volume.

4.Which expression gives the volume of a rectangular prism with length l, width w and height h?

l + w + h
l × w × h
2 × (l + w + h)
l × w ÷ h

Part B — Combine the pieces

A composite solid can be split into simpler prisms. Add their volumes when the pieces fit together without overlapping.

5.A two-part display stand is made from prisms that do not overlap. The base is 5 cm × 3 cm × 2 cm, and the raised block is 4 cm × 2 cm × 3 cm. Find the total volume.

6.A solid is built from unit cubes in a complete rectangular array measuring 3 cubes across, 2 cubes deep and 2 cubes high. How many cubes are there, and what is the solid’s volume?

7.A rectangular-prism tank has a volume of 240 cm³. Its base measures 10 cm by 6 cm. What is its height?

8.A storage unit is made from two non-overlapping rectangular prisms. One has volume 36 cm³ and the other has volume 48 cm³. What is the combined volume?

9.True or false: volume is measured in square units, such as cm².

TrueFalse

10.A small equipment box measures 20 cm × 10 cm × 5 cm. Another box measures 1 m × 0.5 m × 0.25 m. Which box has the greater volume? Convert units so your comparison is fair.

11.A pool at the event is a rectangular prism 25 m long, 10 m wide and 2 m deep. Work out its capacity in cubic metres. Explain why the answer is not in m².