question_answer

The volumes of a cylinder and a cone are in the ratio 3: 1. Find their diameters and then compare them when their heights are equal.

A) Diameter of cylinder = Diameter of cone

B) Diameter of cylinder > Diameter of cone

C) Diameter of cylinder < Diameter of cone

D) Diameter of cylinder = 2 times of diameter

Correct Answer: A

Solution :

Let radii of cylinder and cone be \[{{r}_{1}}\] and \[{{r}_{2}}\]respectively.

Then, \[\frac{\pi r_{1}^{2}h}{\frac{1}{3}\pi r_{2}^{2}h}=\frac{3}{1}\]\[\Rightarrow \]\[\frac{3r_{1}^{2}}{r_{2}^{2}}=\frac{3}{1}\]\[\Rightarrow \]\[{{r}_{1}}={{r}_{2}}\]

\[{{d}_{1}}={{d}_{2}}\]