Geometery project help!?

Question

It gives me the hempispehere and tells me that the Volume is 60 ft and i need to find the total surface area....
HElp?

Answer 1

The total surface area of a hemisphere is found by adding the area of the flat part, which is a circle, to the area of the "dome", which is half the surface area of the entire sphere.

V = (1/2)*(4/3)*PI*r^3 = (2/3)PI*r^3 = 60
so PI*r^3 = 90

radius = cube root of 90/PI

Flat area = PI*r^2 = PI*(cube root of 90/PI)^2
= PI*90^(2/3)/PI^2 = 90(^2/3)/PI

"Dome" area = (1/2)*4PI*r^2 = 2PI*(cube root of 90/PI)^2

= 2(90)^(2/3)/PI

Total surface area = flat area + dome area =
3(90^2/3)/PI

Answer 2

If you are saying that the volume of a hemisphere is 60 cubic feet then you know that the volume of the full sphere is 120 cubic feet. The formula for area is 4/3 x pi x the radius cubed. Solve for the radius. (cube root of 90/pi)

Formula for area is 4 x pi x the radius squared

Plug what you got above for the radius into that formula and you have the area of the whole sphere. The area of the hemisphere is half that.