[tex] \bf \textit{volume of a sphere}\\\\
V=\cfrac{4\pi r^3}{3}~~
\begin{cases}
r=radius\\
-----\\
V=972\pi
\end{cases}\implies 972\pi =\cfrac{4\pi r^3}{3}\implies (3)972\pi =4\pi r^3
\\\\\\
\cfrac{2916\pi }{4\pi }=r^3\implies 729=r^3\implies \sqrt[3]{729}=r\implies 9=r [/tex]
Hope that's an apple pie. Just between us, we want to discuss pi, or [tex] \pi [/tex], or π, not pie.
The formula for the volume of a sphere of radius r is V = (4π/3)*r^3. Since we know that V = 972π, we know that 972π = (4π/3)r^3.
We must solve for r^3, and then solve for r.
To accomplish this, multiply both sides of the equation by 3 / (4π). This results in the equation
(3) 972π
----- * --------- = 729 = r^3.
4π 1
Taking the cube root of both sides of this result, we get r = 9.
The radius of this sphere is 9 units.
