Lucky995idn
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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

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MrRoyalidn

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

The equation of r is: [tex]\mathbf{r = \sqrt{\frac{3V}{\pi h}}}[/tex]

The equation is given as:

[tex]\mathbf{V = \frac 13 \pi r^2h}[/tex]

We start by multiplying both sides by 3

[tex]\mathbf{V \times 3= \frac 13 \pi r^2h \times 3}[/tex]

Rewrite as:

[tex]\mathbf{3V= \pi r^2h}[/tex]

Divide both sides by [tex]\mathbf{\pi h}[/tex]

[tex]\mathbf{\frac{3V}{\pi h}= \frac{\pi r^2h}{\pi h}}[/tex]

Cancel out common factors

[tex]\mathbf{\frac{3V}{\pi h}= r^2}[/tex]

Take square roots of both sides

[tex]\mathbf{\sqrt{\frac{3V}{\pi h}}= \sqrt{r^2}}[/tex]

Evaluate the right-hand sides

[tex]\mathbf{\sqrt{\frac{3V}{\pi h}}= r}[/tex]

Make r the subject

[tex]\mathbf{r = \sqrt{\frac{3V}{\pi h}}}[/tex]

Hence, the resulting equating for r is:

[tex]\mathbf{r = \sqrt{\frac{3V}{\pi h}}}[/tex]

Read more about the subject of formulas at:

https://brainly.com/question/21866313

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