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

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A student in Brisbane is designing a cylindrical can-cooler for a school fundraising project. The cooler is made from a single piece of fabric that wraps around a right circular cylinder with a height of 18 cm and a base radius of 77 cm.

The fabric covers only the lateral surface. What is the exact surface area of the lateral surface of the cylinder, in square centimetres, expressed in terms of π?

Use the formula for lateral surface area of a cylinder: SA = 2πrh, where r is the radius and h is the height.

Circle measurementsradius = 77 cmr = 77 cm
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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 problem asks for the lateral surface area of a right circular cylinder with height h = 18 cm and base radius r = 77 cm.
  2. The lateral surface area of a cylinder is given by the formula SA = 2πrh, which applies to right circular cylinders where the side is perpendicular to the base.
  3. Substitute the given values into the formula: SA = 2 × π × 77 × 18.
  4. First, compute the product of the constants: 2 × 77 × 18.
  5. Calculate 2 × 77 = 154.
  6. Then compute 154 × 18. Break it down: 154 × 10 = 1540, and 154 × 8 = 1232. Add: 1540 + 1232 = 2772.
  7. Now include π: SA = 2772π cm².
  8. The result is expressed exactly in terms of π, as required.
  9. Check the calculation: 2 × 77 × 18 = 2 × 1386 = 2772. Correct.
  10. Verify units: radius and height are in centimetres, so surface area is in square centimetres. Correct.
  11. The lateral surface area is 2772π cm².
  12. This matches the required form: exact value in terms of π, with correct units.

Reference answer: 2772π cm²

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