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The volume V of a sphere is given by V(r)=43r3 where r is the length of the radius. Write a function that gives the radius in terms of the volume.

1 Answer

6 votes

Answer:
r=\sqrt[3]{(3V)/(4\pi)}

Explanation:

Given

The volume of a sphere is given by


V(r)=(4)/(3)\pi r^3

Now isolating
r^3

Divide both sides by
(4)/(3)\pi


\Rightarrow (V(r))/((4)/(3)\pi )=r^3\\\\\Rightarrow r^3=(3V)/(4\pi)\\\\\Rightarrow r=\sqrt[3]{(3V)/(4\pi)}

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