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If the height of a given cone became thrice and the radius of the base remains the same. What is the ratio of the volume of the given cone and the volume of the second cone?
Let radius of given cone = $$r$$ and height = $$h$$
Height of new cone = $$3h$$
Volume of cone = $$\frac{1}{3}\pi r^2h$$
Thus, required ratio = $$\frac{\frac{1}{3}\pi r^2h}{\frac{1}{3}\pi r^2(3h)}=\frac{1}{3}$$
$$\therefore$$ Ratio of the volume of the given cone and the volume of the second cone = 1 : 3
=> Ans - (A)
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