Answer:
[tex]12\pi (inches)^{2}[/tex]
Step-by-step explanation:
Given:
radius of cone = 3 inch
Total area of cone = [tex]24\pi (inch)^{2}[/tex]
Find the volume of the cone?
We know the area of cone = [tex]\pi r(r+s)[/tex] -------(1)
Where r = radius
Ans s = side of the cone
Put the area value in equation 1
[tex]24\pi=\pi r(r+s)[/tex] -------(1)
[tex]\frac{24\pi }{\pi r} =r+s[/tex]
[tex]\frac{24}{ r}-r =s[/tex]
Put r value in above equation.
[tex]s =\frac{24}{ 3}-3[/tex]
[tex]s=8-3[/tex]
[tex]s=5[/tex]
The side s = 5 inches
We know the side of the cone formula
[tex]s^{2}=r^{2}+ h^{2}[/tex]
[tex]h^{2}=s^{2}- r^{2}[/tex]
Put r and s value in above equation.
[tex]h^{2}=5^{2}- 3^{2}[/tex]
[tex]r^{2} = 25-9[/tex]
[tex]r^{2} = 16[/tex]
[tex]r = 4[/tex]
The volume of cone is
[tex]V = \frac{1}{3} \pi r^{2} h[/tex]
Put r and h value in above equation.
[tex]V = \frac{1}{3} \pi (3)^{2}\times 4[/tex]
[tex]V = 12\pi (inches)^{2}[/tex]
The Volume of the cone is [tex]12\pi (inches)^{2}[/tex]
