Question

A cone with a radius of 3" has a total area of 24 pi sq. in. Find the volume of the cone.

24 pi
15 pi
12 pi

Answer 1

12pi is he answer.
Pi.r.l+pir^2=24pi
r=3 if you plug this you get l=5
h^2+r^2=l^2
so h=4
V=(1/3)pir^2 . h =(1/3)pi . 9.4=12pi

Answer 2

Answer:

the volume of the cone 12 pi.

Step-by-step :

Given : A cone with a radius of 3" has a total area of 24 pi sq. in.

To find: . Find the volume of the cone.

Formula used : Area =  pi × radius × length + pi × $radius^{2}$ .

                   $height^{2} +radius^{2} = lenght^{2}$.

                       Volume = $\frac{1}{3}× radius^{2}$× height.

Solution :  24 pi = pi×3 × length + pi × $2^{2}$ .

                length = 5.

$height^{2} +3^{2} = 5^{2}$.

Height = 4.

So,  Volume = $\frac{1}{3}× 3^{2}$× 4.

 Volume  = 12 pi.

Therefore, the volume of the cone 12 pi.