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4024/22 May/Jun 2020, Question 8: Surface Area of a Cuboid and Cylinder

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 8 marks

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The question, in short

Work with a cylindrical birthday cake of radius 10 cm made of two 3 cm cake layers separated by a 12 mm icing layer; find icing volume, chocolate-covered area, and a slice's sector angle.

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Part (a) · 2 marks

Calculate the volume of the 12 mm icing layer, radius 10 cm, giving the answer in cm³.

  1. 112 mm = 1.2 cm
  2. 2Volume = π × 10² × 1.2 = 376.99… ≈ 377.0 cm³

Answer376.99 to 377.04

Part (b) · 3 marks

Calculate the total area covered with chocolate on the top and curved surface of the cake.

  1. 1Total height = 3 + 3 + 1.2 = 7.2 cm
  2. 2Area = π × 10² + 2 × π × 10 × 7.2
  3. 3= 100π + 144π = 244π = 766.5… ≈ 767 cm²

Answer767 or 766.5 to 766.6…

Part (c) · 3 marks

For a prism slice of height 7.5 cm, top sector radius 10.3 cm and volume 200 cm³, calculate angle x.

  1. 1x/360 × π × 10.3² × 7.5 = 200
  2. 2x = 200 × 360 ÷ (π × 10.3² × 7.5)
  3. 3x = 28.803… ≈ 28.80

Answer28.79 to 28.80…

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