Question

The volume of a right circular cone is found using the equation V = 1 3 π r 2 h . Which equation represents the volume solved for r ? r = √ π V 3 h r = √ π V 3 h r = √ V h 3 π r is equal to square root of cap v h over 3 pi end root r = √ 3 π V h r is equal to square root of 3 pi over cap v h end root r = √ 3 V π h r = √ 3 V π h

Answer 1

Solving for a variable in an equation means, we are changing the subject of formula of the equation.

The equation of r is: $\mathbf{r = \sqrt{\frac{3V}{\pi h}}}$

The equation is given as:

$\mathbf{V = \frac 13 \pi r^2h}$

We start by multiplying both sides by 3

$\mathbf{V \times 3= \frac 13 \pi r^2h \times 3}$

Rewrite as:

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

Divide both sides by $\mathbf{\pi h}$

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

Cancel out common factors

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

Take square roots of both sides

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

Evaluate the right-hand sides

$\mathbf{\sqrt{\frac{3V}{\pi h}}= r}$

Make r the subject

$\mathbf{r = \sqrt{\frac{3V}{\pi h}}}$

Hence, the resulting equating for r is:

$\mathbf{r = \sqrt{\frac{3V}{\pi h}}}$

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