Question 23

If the height and base radius of a cone are increased by 50% and 25% respectively then the ratio between the volume of a given cone and the new cone is

Solution

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Let us assume the earlier height and radius of the cone to be 100 and 100 units respectively.
Height and radius of the new cone = 150 and 125 units respectively.
Ratio of volumes = $$\frac{1}{3}\pi\ 100^2\times\ 100\ :\ \frac{1}{3}\pi\ 125^2\times\ 150\ =100^3\ :\ 125^2\times\ 150\ =\ 32:75$$

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