We need the radius to find the volume and we can find the radius using the formula for surface area.
The formula for the surface area of a sphere is 4*pi*r^2 and we know this is equal to 900*pi. This gives us an equation of 4r^2 = 900 if we eliminate the pi on both sides of the equation. We divide by 4 to get r^2 = 225. Then we have to take the square root of both sides to get r = 3.
The formula for the volume of a sphere is (4/3)*pi*r^3 and now we plug the radius into this formula to get (4/3)*pi*(15)^3. If we simplify the exponent we get (4/3)*pi*3375. Since we typically leave our answers in terms of pi, we multiply the (4/3) by our 3375 to simplify our answer and get 4500*pi.
The volume of a sphere with a surface area of 900 pi is 4500 pi.
May 5th, 2015
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