How to find the diameter of a sphere - PSAT Math

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Question

If a sphere has an approximate volume of $904.32\textup{ cubic meters}$ , then what is the approximate diameter of this sphere?

Answer

The formula for the volume of a sphere is

$v=\left ( \frac{4}{3} \right )\pi r^3$

Therefore,

$904.32=\left ( \frac{4}{3} \right )\pi r^3$

Dividing both sides by $\left ( \frac{4}{3} \right )\pi$ , leaves us with $r^3\approx215.89$ . Taking the cube root, we find $r\approx5.999$ , meaning our diameter $d\approx12$ .

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