The volume of a cone is 141.3 cubic inches. The height of the cone is...

The formula for the Volume of a cone is:
${\displaystyle V=\pi r^2\frac{h}{3}}$
Where:
${\displaystyle V}$ is the Volume of the cone: ${\displaystyle 141.3{\text{in}}^3}$ for this problem.
${\displaystyle r}$ is the radius of the cone: what we are solving for in this problem.
${\displaystyle h}$ is the height of the cone: ${\displaystyle 15\text{in}}$ for this problem.
Substituting and solving for ${\displaystyle r}$ gives:
${\displaystyle 141.3{\text{in}}^3=\pi \times r^2\times \frac{15\text{in}}{3}}$
${\displaystyle 141.3{\text{in}}^3=\pi \times r^2\times 5\text{in}}$
${\displaystyle \frac{141.3{\text{in}}^3}{5\text{in}}=\frac{\pi \times r^2\times 5\text{in}}{5\text{in}}}$
${\displaystyle \frac{141.3{\text{in}}^{\cancel{3}2}}{5\cancel{\text{in}}}=\frac{\pi \times r^2\times \cancel{5\text{in}}}{\cancel{5\text{in}}}}$
${\displaystyle \frac{141.3{\text{in}}^2}{5}=\pi r^2}$
${\displaystyle 28.26{\text{in}}^2=\pi r^2}$
${\displaystyle \frac{28.26{\text{in}}^2}{\pi }=\frac{\pi r^2}{\pi }}$
${\displaystyle \frac{28.26{\text{in}}^2}{\pi }=\frac{\cancel{\pi }{r}^2}{\cancel{\pi }}}$
${\displaystyle \frac{28.26{\text{in}}^2}{\pi }=r^2}$
We can use 3.1416 to estimate ${\displaystyle \pi }$ giving:
${\displaystyle \frac{28.26{\text{in}}^2}{3.1416}=r^2}$
${\displaystyle 9{\text{in}}^2=r^2}$ rounded to the nearest inch.
To calculate the radius of the cone while keeping the equation balanced, take the square root of each side of the equation:
${\displaystyle \sqrt{9{\text{in}}^2}=\sqrt{r^2}}$
${\displaystyle 3\text{in}=r}$
${\displaystyle r=3\text{in}}$
The cone's radius is 3 inches, rounded to the nearest inch.