Ratios of Similar Solids: From Area to Volume

Ratios of Similar Solids: From Area to Volume

TGM Original

The diagram shows two geometrically similar pots with a circular base.
It is given that the height of pot \(A\) is \(30\) cm and the base area of pot \(B\) is \(\frac{4}{9}\) of the base area of pot \(A\).

  1. Calculate the height of pot \(B\).
  2. The curved surface area of pot \(B\) is \(260\) cm\({}^2\).
    Find the curved surface area of pot \(A\).
  3. If the capacity of pot \(A\) is \(5.4\) litres, find the capacity of pot \(B\), giving your answer in cm\({}^3\).

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Answer:(i) \(20\text{ cm}\) (ii) \(585\text{ cm}^2\) (iii) \(1600\text{ cm}^3\)

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