### Home > INT2 > Chapter 11 > Lesson 11.2.1 > Problem11-52

11-52.

Solve each of the following equations for the indicated variable.

1. The formula $V =\frac { 1 } { 3 }πr^2h$ gives the volume of a cone with radius $r$ and height $h$. Solve $V =\frac { 1 } { 3 }πr^2h$ for $h$.

Multiply both sides by $3$ to remove the fraction.

Divide both sides by $πr^2$.

$\frac{3V}{\pi r^2} = h$

2. When an object is in motion, the energy that it has due to its motion is called kinetic energy. The formula $K =\frac { 1 } { 2 }mv^2$ gives the kinetic energy of an object with mass $m$ and velocity $v$. Solve $K =\frac { 1 } { 2 }mv^2$ for $v$.

Use the same method as part (a).