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4024/22 May/Jun 2021, Question 9: Volume and Surface Area of a Cone

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 7 marks

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The question, in short

Cone with radius 6 cm and slant height l has total surface area 84π cm²; show l = 8, find the volume, and find the radius of a similar cone with total surface area 47.25π cm².

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Part (a) · 2 marks

Use the total surface area formula with radius 6 and area 84π to show that the slant height l equals 8.

  1. 1Total surface area = πrl + πr²
  2. 26πl + π × 6² = 84π
  3. 36πl = 84π − 36π = 48π
  4. 4l = 8

Answer6πl + π × 6² = 84π leading to l = 8, or 6πl = 84π − π × 6² leading to l = 8

Part (b) · 3 marks

Calculate the volume of the cone using radius 6 and the slant height from part a.

  1. 1h = √(8² − 6²) = √28
  2. 2V = 1/3 × π × 6² × √28
  3. 3= 199.48… ≈ 199.5 cm³

Answer199 or 200 or 199.4 to 199.5…

Part (c) · 2 marks

For a similar cone with total surface area 47.25π cm², find its radius.

  1. 1Area scale factor = 47.25π/84π = 0.5625
  2. 2Length scale factor = √0.5625 = 0.75
  3. 3Radius = 6 × 0.75 = 4.5 cm

Answer4.5

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Also searched as: 4024/22/M/J/21 · 4024_s21_qp_22 · 4024 s21 22 · question 9.
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