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4MA1/1H Jun 2019, Question 17: Area Factor of Similar Shapes

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 4 marks

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The question, in short

Two similar vases, A and B, have heights 24 cm and 36 cm; A's surface area is 960 cm². Find B's surface area, then express A's volume in terms of B's volume V.

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Part (a) · 2 marks

Using the heights 24 cm and 36 cm, calculate the surface area of vase B, given vase A's surface area is 960 cm².

  1. 1Length scale factor = 36 ÷ 24 = 1.5
  2. 2Area scale factor = 1.5² = 2.25
  3. 3Surface area of B = 960 × 2.25 = 2160

Answer2160

Part (b) · 2 marks

Given vase B's volume is V cm³, write an expression for vase A's volume in cm³, using V.

  1. 1Length scale factor from B to A = 24 ÷ 36 = 2/3
  2. 2Volume scale factor = (2/3)³ = 8/27
  3. 3Volume of A = (8/27)V

Answer(8/27)V

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