Question

a cone with a radius of 3” has a total area of 24pie square inches. Find the volume of the cone. 12pie, 24 pie or 15 pie

Answer 1

`12\pi (inches)^(2)`

Explanation:

Given:

radius of cone = 3 inch

Total area of cone =
`24\pi (inch)^(2)`

Find the volume of the cone?

We know the area of cone =
`\pi r(r+s)` -------(1)

Where r = radius

Ans s = side of the cone

Put the area value in equation 1

`24\pi=\pi r(r+s)` -------(1)

`(24\pi )/(\pi r) =r+s`

`(24)/( r)-r =s`

Put r value in above equation.

`s =(24)/( 3)-3`

`s=8-3`

`s=5`

The side s = 5 inches

We know the side of the cone formula

`s^(2)=r^(2)+ h^(2)`

`h^(2)=s^(2)- r^(2)`

Put r and s value in above equation.

`h^(2)=5^(2)- 3^(2)`

`r^(2) = 25-9`

`r^(2) = 16`

`r = 4`

The volume of cone is

`V = (1)/(3) \pi r^(2) h`

Put r and h value in above equation.

`V = (1)/(3) \pi (3)^(2)* 4`

`V = 12\pi (inches)^(2)`

The Volume of the cone is
`12\pi (inches)^(2)`