Question

2 cylinders have their radii into ratio 4:7. If their heights are in the ration of 21:8 then their volumes would be in what ratio

Answer 1

Answer

2 cylinders have their volume into ratio 6 : 7

Explanation

Volume of a cylinder

Ler r be the radius  and h be the heights of a cylinder, The volume of cylinder can be written as

       V = π$r^{2}$h

It is given that,

2 cylinders have their radii into ratio 4:7.

Radius be 4x and 7x

And their heights are in the ration of 21:8

Heights be, 21h and 8h

Let v1 be the volume of cylinder with radius 4x and height 21h

and v2 be the volume of cylinder with radius 7x and height 8h

Therefore

v1 =π$(4x)^{2}$21

v2 =π$(7x)^{2}$8

From this we get,

$\frac{v1}{v2}$ = $\frac{6}{7}$

2 cylinders have their volume into ratio 6 : 7

Answer 2

Given radii of 2 cylinders are in the ratio 4:7

and their height are in the ratio 21:8

Volume of the cylinder is given by

 V = π r^2 h

r is given by 4x and 7x

h is given by 21 and 8

Now V1 = π (4x)^2 21

       V2 = π (7x)^2 8

V1 / V2 = π (4x)^2 21 /  π (7x)^2 8

We get 6/7 and keeping in the ratio form it will be 6 : 7