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Question:

The value of each of a set of coins varies as the square of its diameter, if its thickness remains constant, and it varies as the thickness, if the diameter remains constant. If the diameter of two coins are in the ratio 4 : 3, what should be the ratio of their thickness if the value of the first is four times that of the second?

Explanation:

Let D₁, T₁ and D₂, T₂ denote the diameters and the thickness of the two coins respectively. If V₁ and V₂are the values of the two coins.

$\frac{V_{1}}{V_{2}} = (\frac{{D_{1}}^{2} T_{1}}{{D_{2}}^{2} T_{2}}) = {(\frac{D_{1}}{D_{2}})}^{2} (\frac{T_{1}}{T_{2}})$

Therefore, $\frac{4}{1} = {(\frac{4}{3})}^{2} (\frac{T_{1}}{T_{2}}) \Rightarrow (\frac{T_{1}}{T_{2}}) = \frac{9}{4}$

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