SOLUTION: a sphere has a volume of 4500pi cubic inches. find the surface area of the sphere.

Algebra ->  Surface-area -> SOLUTION: a sphere has a volume of 4500pi cubic inches. find the surface area of the sphere.       Log On


   

Question 878968: a sphere has a volume of 4500pi cubic inches. find the surface area of the sphere.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Handy Formulas (memorize them or have them on a sheet of paper for reference)


Volume of Sphere: V+=+%284%2F3%29%2Api%2Ar%5E3


Surface Area of Sphere: SA+=+4%2Api%2Ar%5E2


-------------------------------------------------------


First start with the volume of a sphere and use the given volume to solve for the radius r.


V+=+%284%2F3%29%2Api%2Ar%5E3


4500pi+=+%284%2F3%29%2Api%2Ar%5E3


4500pi%2Fpi+=+%28%284%2F3%29%2Api%2Ar%5E3%29%2Fpi


4500+=+%284%2F3%29%2Ar%5E3


4500%2A3+=+3%2A%284%2F3%29%2Ar%5E3


13500+=+4%2Ar%5E3


13500%2F4+=+%284%2Ar%5E3%29%2F4


3375+=+r%5E3


r%5E3+=+3375


root%283%2Cr%5E3%29+=+root%283%2C3375%29


r+=+15


So the radius of this sphere is 15 inches.


-------------------------------------------------------


Now we use this radius to find the surface area


SA+=+4%2Api%2Ar%5E2


SA+=+4%2Api%2A15%5E2


SA+=+4%2Api%2A225


SA+=+4%2A225%2Api


SA+=+900pi <--- Exact Surface Area


SA+=+900%283.14%29


SA+=+2826 <--- Approximate Surface Area (based on the approximation pi+=+3.14)