Question

express the following statement as an equation involving the indicated variables. the volume v of a sphere is $\frac{4}{3}$ times $pi$ times the cube of the radius r. the volume v of a sphere is given by v = $\frac{4}{3}+pi + r^{3}$. v = $(\frac{4}{3}pi r)^{3}$. v = $\frac{4}{3}pi r^{3}$.

Explanation:

Step1: Translate the statement

The statement says "The volume V of a sphere is $\frac{4}{3}$ times $\pi$ times the cube of the radius r". In mathematical - language, "times" means multiplication.
So the equation is $V=\frac{4}{3}\times\pi\times r^{3}$, which simplifies to $V = \frac{4}{3}\pi r^{3}$.

Answer:

$V=\frac{4}{3}\pi r^{3}$