Problem 100 - College Algebra Essentials

Question

Solve each equation. $$ \text { Solve for } V: r=\sqrt{\frac{3 V}{\pi h}} $$

Step-by-Step Solution

Answer

To solve the given equation for V, the solution is \(V= \frac{\pi h r^2}{3}\).

Step 1: Squaring both sides of the equation

To remove the square root from the right side of the equation, square both sides of the equation. This results in \(r^2=\frac{3 V}{\pi h}\)

Step 2: Isolating 'V' on one side of the equation

The final step is to isolate V on one side of the equation. This will involve manipulating the equation to move V alone to one side of the equation and the other terms to the other side of the equation. This can be done by cross multiplying \(r^2\) and \(\pi h\) and then dividing by 3. The resulting equation is \(V= \frac{\pi h r^2}{3}\)