Question

The volume of a sphere is 5100π
calculate the radius

Answer 1

r = 15

Explanation:

4/3πr³ = 5100

multiply each side of the equation to isolate r³

3/4 x 5100π = πr³

3825π = πr³

r³ = 3825

r = ∛3825

r = 15 when estimated

Answer 2

`\textit{Volume of a Sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=5100\pi \end{cases}\implies 5100\pi =\cfrac{4\pi r^3}{3}\implies 3(5100\pi )=4\pi r^3 \\\\\\ \cfrac{3(5100\pi )}{4\pi }=r^3\implies 3825=r^3\implies \sqrt[3]{3825}=r\implies 15.64\approx r`