If a cylinder and cone have bases of equal radii and are equal heights

1.	If a cylinder and cone have bases of equal radii and are equal heights, then the ratio of their volumes isA) 1 : 3 B) 2 : 3 C) 3 : 1 D) 3 : 2
Answer» Correct option is: C) 3 : 1 Let the radii of both cylinder and cone be r and the heights of both cylinder and cone be h. \(\therefore\) Volume of cylinder is \(V_1 = \pi r^2h\) Volume of cone is \(V_2 = \frac 13 \pi r^2 h\). Ration of their volumes = \(\frac {V_1}{V_2}\) = \(\frac {\pi r^2h}{\frac 13 \pi r^2h}\) =\(\frac 31\) = 3 : 1 Hence, the ratio of their volumes is 3:1. Correct option is: C) 3 : 1

If a cylinder and cone have bases of equal radii and are equal heights, then the ratio of their volumes isA) 1 : 3 B) 2 : 3 C) 3 : 1 D) 3 : 2

Answer»

Correct option is: C) 3 : 1

Let the radii of both cylinder and cone be r

and the heights of both cylinder and cone be h.

\(\therefore\) Volume of cylinder is \(V_1 = \pi r^2h\)

Volume of cone is \(V_2 = \frac 13 \pi r^2 h\).

Ration of their volumes = \(\frac {V_1}{V_2}\) = \(\frac {\pi r^2h}{\frac 13 \pi r^2h}\) =\(\frac 31\) = 3 : 1

Hence, the ratio of their volumes is 3:1.

Correct option is: C) 3 : 1