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

Answer:

$12\pi (inches)^{2}$

Step-by-step 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)

$\frac{24\pi }{\pi r} =r+s$

$\frac{24}{ r}-r =s$

Put r value in above equation.

$s =\frac{24}{ 3}-3$

$s=8-3$

$s=5$

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

$V = \frac{1}{3} \pi r^{2} h$

Put r and h value in above equation.

$V = \frac{1}{3} \pi (3)^{2}\times 4$

$V = 12\pi (inches)^{2}$

The Volume of the cone is $12\pi (inches)^{2}$