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

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 =
`(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 =
`(1)/(3)× 3^(2)`× 4.

Volume = 12 pi.

Therefore, the volume of the cone 12 pi.