Question

The volume of a right circular cylinder with its height equal to the radius is `25 1/7` cm³. Find the height of the cylinder.

The volume of a right circular cylinder with its height equal to the radius is `25 1/7` cm³. Find the height of the cylinder. `("Use"  π = 22/7)`

Answer 1

We have,

Height = Base radius i.e. h = r

As, 

Volume of the cylinder = `25"1"/7 "cm"^3`

`=> 22/7 xx "h"^2 xx "h" = 176/7`

`=> 22/7 xx "h"^2 xx "h" = 176/7`

`=> "h"^3 = (176 xx 7)/(7 xx 22)`

`=> "h"^3 = 8`

`=> "h" = root(3)(8)`

∴ h = 2 cm

So, the height of the cylinder is 2 cm.

Answer 2

Given,

Volume of a right circular cylinder = `25 1/7` cm

i.e., `πr^2h = 176/7`

Where height, h = radius r, then

⇒ `22/7 xx h^2 xx h = 176/7`

⇒ `h^3 = 176/22`

⇒ h³ = 8

⇒ h = 2

Hence, height of the cylinder = 2 cm.