Question

The height of a cylinder is twice the radius of its base. What expression represents the volume of the cylinder, in cubic units?

Answer 1

2πr³

Explanation:

The volume (V) of a cylinder is calculated as

V = πr²h ← r is the radius and h the height

Here h = 2r, hence

V = πr² × 2r = 2πr³

Answer 2

`V'=2\pi r^3\ cubic\ units`

Explanation:

Let h is the height of the cylinder and r is the radius of its base. The expression for the volume of the cylinder is given by :

`V=\pi r^2h`

The height of a cylinder is twice the radius of its base. h' = 2 × r. New volume becomes :

`V'=\pi r^2h'`

`V'=\pi r^2(2r)`

`V'=2\pi r^3\ cubic\ units`

So, the volume of the cylinder is
`2\pi r^3\ cubic\ units`. Hence, this is the required solution.