Question

A cone and cylinder are of the same height their radii of the base are in the ratio 2:1. Find the radius of their volumes

Answer 1

Find the attachment

Answer 2

Given,

Cone and cylinder have the same height.

The ratio of their radius =  2:1

To Find,

The ratio of cone and cylinder volume.

Solution,

The height of the cone and cylinder are the same.

Let, height be h

The radius ratio of cone and cylinder =

2:1

Let, the radii of the cone =2x

Radii of cylinder = x

The volume of the cone =

$\frac{\pi *r*r}{3}$  = $\frac{\pi *2x*2x}{3}$

The volume of the cylinder =

$\pi$r²h =$\pi$*x*x*h

The volume of cone: Volume of cylinder=

$\frac{\pi *2x*2x*h}{3}$ : $\pi$*x*x*h

$\frac{1}{3}$×$\pi$*4x²*h = $\pi$*x²h

Let's, divide it.

$\frac{4}{3}$    = 4:3

The ratio of the volume of the cone and cylinder is 4:3