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To find the volume of a cone, we use the formula V= 13r2h, where V is the volume, r is the radius of the circle of the base, and h is the height of the cone. Rewrite the equation so that the positive value of r is written in terms of V and h. I need help with this problem.

Answer :

MrRoyal

Answer:

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

Step-by-step explanation:

Given

[tex]V = \frac{1}{3}\pi r^2h[/tex]

Required

Solve for r

[tex]V = \frac{1}{3}\pi r^2h[/tex]

Multiply both sides by 3

[tex]3 * V = \frac{1}{3}\pi r^2h * 3[/tex]

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

Divide both sides by [tex]\pi h[/tex]

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

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

Take square root of both sides

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

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

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

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