NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Surface area and volume

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A school in Perth is ordering custom-made rectangular prisms to store art supplies. Each prism has a length of 44 cm, a width of 60 cm, and a height of 22 cm.

Calculate the exact surface area of one prism in square centimetres using the formula SA = 2(lw + lh + wh). Provide the exact answer as a simplified integer or fraction.

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. Identify the given dimensions: length (l) = 44 cm, width (w) = 60 cm, height (h) = 22 cm.
  2. The formula for surface area of a rectangular prism is SA = 2(lw + lh + wh). This formula accounts for all six faces: two of each pair of opposite faces.
  3. Calculate the area of the front and back faces: lw = 44 × 60. 44 × 60 = 2640 cm².
  4. Calculate the area of the left and right faces: lh = 44 × 22. 44 × 22 = 968 cm².
  5. Calculate the area of the top and bottom faces: wh = 60 × 22. 60 × 22 = 1320 cm².
  6. Sum the three face areas: lw + lh + wh = 2640 + 968 + 1320. 2640 + 968 = 3608; 3608 + 1320 = 4928 cm².
  7. Multiply the sum by 2 to get the total surface area: SA = 2 × 4928. 2 × 4928 = 9856 cm².
  8. Verify the arithmetic: 2 × 4928 = 9856. This is correct.
  9. The surface area is 9856 cm². This is an exact integer, so no simplification is needed.
  10. Check units: all dimensions are in centimetres, so surface area is in square centimetres (cm²). Correct.
  11. Confirm the shape is a right rectangular prism, so the formula applies directly.
  12. The surface area of one prism is exactly 9856 cm².

Reference answer: 9856 cm²

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