Solve the following formula for $h$
$V=\frac{\pi r^2 h}{3}$
A. $h=\sqrt{\frac{3 V}{r^2 \pi}}$
B. $h=\frac{3 V}{r^2 \pi}$
C. $h=\frac{r^2 \pi}{3 V}$
D. $h=\frac{3 V}{2 r \pi}$
Answer (1)
Multiply both sides of the equation by 3: 3 V = π r 2 h
Divide both sides of the equation by π r 2 : h = π r 2 3 V
The solution for h is h = π r 2 3 V
The correct answer is h = r 2 π 3 V
Explanation
Understanding the Problem We are given the formula V = 3 π r 2 h and we want to solve for h . This means we want to isolate h on one side of the equation.
Multiply by 3 First, we multiply both sides of the equation by 3 to get rid of the fraction: 3 × V = 3 × 3 π r 2 h 3 V = π r 2 h
Divide by π r 2 Next, we divide both sides of the equation by π r 2 to isolate h : π r 2 3 V = π r 2 π r 2 h h = π r 2 3 V
Final Answer Therefore, the solution for h is h = π r 2 3 V . Comparing this to the given options, we see that it matches option B.
Examples
Imagine you are designing a cone-shaped container for ice cream. You know the desired volume V of the ice cream and the radius r of the cone's base. By solving the formula V = 3 π r 2 h for h , you can determine the height h of the cone needed to hold the specified volume of ice cream. This ensures that the container is perfectly sized for your delicious treat. For example, if you want a volume of V = 100 cm 3 and a radius of r = 3 cm , then the height would be h = π × 3 2 3 × 100 ≈ 10.61 cm .
