Question

The height and the base radius of a cone and cylinder are equal. Show that their volumes

are in the ratio of 3 : 1.​

Answer 1

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Let h and r be the height and radius of the cone respectively.

Given that the height and the base radius of a Cone and Cylinder are equal to the radius of the Sphere.

Therefore,

Radius of sylinder = r

Height of cylinder = h

Volume of cone (V1) :- $\frac{1}{3}\pi {r}^{2}h.....(1)$

Volume of cylinder (V2) :- $\pi {r}^{2}h.....(2)$

Dividing equation (1) by (2), we have

$\frac{v1}{v2} = \frac{ \frac{1}{3}\pi {r}^{2}h }{\pi {r}^{2}h }$

$⇒ \frac{v1}{v2} = \frac{1}{3}$

Hence, the ratio of the volume of cone to that of cylinder is 1:3.

Answer 2

Answer:

I have attached the solution as picture format please refer to that :)