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Question

Mark the correct alternative of the following:
A right circular cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is?

A
$$3:5$$
B
$$3:1$$
C
$$1:3$$
D
$$2:5$$
Solution
Verified by Toppr

Correct option is D. $$1:3$$
It is given that, the volumes of both cylinder and cone are the same.
So, let volume of the cylinder and cone be $$V.$$
It is also given that, their base radii are the same.
So, let radius of the cylinder $$=$$ Radius of the cone $$=r$$
Let the height of the cylinder and the cone be $$h_1$$ and $$h_2$$ respectively.
Volume of cone $$=\dfrac{1}{3}\pi r^2 h_2$$
Volume of cylinder $$=\pi r^2 h_1$$
We know both volumes are same.
$$\therefore$$ $$\dfrac{1}{3}\pi r^2 h_2=\pi r^2 h_1$$

$$\Rightarrow$$ $$\dfrac{h_1}{h_2}=\dfrac{\pi r^2}{3\pi r^2}$$

$$\therefore$$ $$\dfrac{h_1}{h_2}=\dfrac{1}{3}$$

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