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
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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