Question

the volume of a sphere is given by the formula $v = \frac{4}{3}\pi r^{3}$ and is 113 m³. what is the radius, to the nearest meter, of this sphere? a. 3 m b. 5 m c. 7 m d. 9 m

Explanation:

Step1: Substitute volume value into formula

Given $V = \frac{4}{3}\pi r^{3}$ and $V = 113$, we have $113=\frac{4}{3}\pi r^{3}$.

Step2: Solve for $r^{3}$

First, multiply both sides by $\frac{3}{4\pi}$: $r^{3}=\frac{113\times3}{4\pi}$.
Calculate $\frac{113\times3}{4\pi}=\frac{339}{4\pi}\approx\frac{339}{4\times3.14}\approx\frac{339}{12.56}\approx 27$.

Step3: Solve for $r$

Take the cube - root of both sides: $r=\sqrt[3]{r^{3}}$. Since $r^{3}\approx27$, then $r=\sqrt[3]{27}=3$.

Answer:

A. 3 m