whats the volume of a sphere with a surface area of 900 pie

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whats the volume of a sphere with a surface area of 900 pie 

May 5th, 2015

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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