Question

A cone with a radius of 12 cm and a height of 12 cm has the same volume as a cylinder with a radius of 8 cm. What is the height of the cylinder?

Answer 1

Height(h) of the cylinder is:
`h=9cm`

Explanation:

Height(H) of cone = 12 cm

Radius(R) of the cone =12 cm

Radius(r) of the cylinder=8 cm

Height(h) of the cylinder=?

Volume of the cone=Volume of the cylinder

`\pi *R^2*(H)/(3) =\pi *r^2*h`

Dividing by '
`\pi`' both sides:

`R^2*(H)/(3)=r^2*h`

Putting the values in the formula:

`12^2*(12)/(3)= 8^2*h`

`144*4=64*h\\\\576=64*h\\\\`

Dividing by '64' both sides:

`h=576/64`

`h=9cm`

The height(h) of the cylinder is :
`h=9cm`