The base of cone is a circle.
The formula of area of a circle: [tex]A_O=\pi r^2[/tex]
We have:
[tex]A_O=9\pi[/tex]
Calculate the length of radius r:
[tex]\pi r^2=9\pi\ \ \ \ |:\pi\\\\r^2=9\to r=\sqrt9\to r=3[/tex]
The formula of a volume of a cone:
[tex]V=\dfrac{1}{3}Bh[/tex]
Substitute:
[tex]B=9\pi,\ h=4\\\\V=\dfrac{1}{3}\cdot9\pi\cdot4=3\pi\cdot4=12\pi[/tex]
The formula of a surface area of a cone:
[tex]SA=B+\pi rl[/tex]
We need a length of l. Use the Pythagorean theorem:
[tex]l^2=r^2+h^2\\\\l^2=3^2+4^2\\\\l^2=9+16\\\\l^2=25\to l=\sqrt{25}\to l=5[/tex]
Calculate the surface area:
[tex]SA=9\pi+\pi\cdot3\cdot5=9\pi+15\pi=24\pi[/tex]
Answer: V = 12π, SA = 24π
