NavGanitMateby NavGreen Compute, AustraliaBased on Victorian Curriculum Mathematics v2.0
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Volume and capacity of prisms

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Required skills (click to reveal)

A craft designer in Brisbane is creating a custom rectangular prism-shaped display box for a sculpture. The internal dimensions of the box are 23 cm in length, 53 cm in width, and 18 cm in height.

The designer needs to determine the exact capacity of the box in litres. (Note: 1 litre = 1000 cm³.) What is the exact capacity of the box in litres?

Concept illustrations

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A rectangular prism. A prism of length 4 cm, width 3 cm and height 2 cm has volume 24 cm³ = 24 mL. The perspective drawing is schematic.4 cm3 cm2 cm
A prism of length 4 cm, width 3 cm and height 2 cm has volume 24 cm³ = 24 mL. The perspective drawing is schematic.
Square the length conversion factor. A 1 m by 1 m square is 100 cm by 100 cm. Its area is 10,000 cm². The 10-by-10 grid shows 100 squares, each 10 cm by 10 cm.1 m = 100 cm1 m100 cm
A 1 m by 1 m square is 100 cm by 100 cm. Its area is 10,000 cm². The 10-by-10 grid shows 100 squares, each 10 cm by 10 cm.

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Formula

Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The internal dimensions of the rectangular prism-shaped box are given as length = 23 cm, width = 53 cm, and height = 18 cm.
  2. The volume of a rectangular prism is calculated using the formula: volume = length × width × height.
  3. Substitute the given values into the formula: volume = 23 cm × 53 cm × 18 cm.
  4. First, compute 23 × 53: 23 × 50 = 1150, and 23 × 3 = 69; so 1150 + 69 = 1219.
  5. Now multiply 1219 × 18: break 18 into 10 + 8, so 1219 × 10 = 12190, and 1219 × 8 = 9752.
  6. Add the two products: 12190 + 9752 = 21942.
  7. The volume is 21942 cm³.
  8. Convert cubic centimetres to litres using the conversion: 1 litre = 1000 cm³.
  9. Divide the volume in cm³ by 1000: 21942 ÷ 1000 = 21.942.
  10. The capacity is 21.942 litres.
  11. The question asks for the exact capacity in litres, so the answer is 21.942 litres.
  12. Check: 21.942 × 1000 = 21942 cm³, which matches the original volume. The calculation is correct.

Reference answer: 21.942 litres

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