Finding Area of Sphere

stevecowall

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Nov 9, 2011
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Question: A sphere has the same numerical value for both its surface area and its volume. Find the radius of the sphere.
My solution: 4πr^2 = 4/3πr^3 but the question say it has to be numerical value. And that is why I got stuck at.

Thanks,
 
Last edited:
"numerically equal" usually means only to ignore the units.

\(\displaystyle 4\pi r^2 = \frac{4}{3}\pi r^{3}\)

That's great. Now, solve for a non-useless 'r'.

\(\displaystyle \pi r^2 = \frac{1}{3}\pi r^{3}\)

\(\displaystyle r^2 = \frac{1}{3} r^{3}\)

\(\displaystyle r \ne 0\), since that is boring.

\(\displaystyle 1 = \frac{1}{3} r\)

Are we close?
 
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