Problem involving Similar Solids

Problem involving Similar Solids

Secondary 3

The diagram shows three geometrically similar flasks \(A\), \(B\) and \(C\) with a circular base of diameter \(4\) cm, \(x\) cm and \(2.5\) cm respectively.

The heights of flasks \(A\) and \(B\) are \(20\) cm and \(18\) cm respectively.

Find

the diameter, \(x\) cm, of the base of flask \(B\) ,
\(\frac{\text{surface area of flask}\hspace{0.5em} B}{\text{surface area of flask}\hspace{0.5em} A}\) ,
\(\frac{\text{volume of flask}\hspace{0.5em} C}{\text{volume of flask}\hspace{0.5em} A}\) .

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Answer:\(\text{(i)}\ x=3.6\text{ cm}\) \(\text{(ii)}\ \dfrac{81}{100}\) \(\text{(iii)}\ \dfrac{125}{512}\)

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