Question

The volume of the right cone below is 448π units^3. Find the value of x

Answer 1

The radius of the cone is x = 8 units.

Let's find the value of x.

The volume of a cone of height H and radius R is:

V = (1/3)*π*R²*H

Here we have.

R = x

H =21

V = 448π

Replacing that we get:

448π = (1/3)*π*x²*21

remove pi from both sides:

448 = (1/3)*x²*21

Now solve this for x:

x = √( 3*448/21)

x = 8 units.

Answer 2

Volume of the cone = 448π units³

The formula of the volume is given by:

`V=(1)/(3)hπr²`

Hence:

`448\pi=(1)/(3)*21*\pi* x^2`

Solving for x:

`x=\sqrt{(3*448)/(21)}=8`

ANSWER

x = 8