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V=pir^(2)h
The equation gives the Volume
V of a right cylinder with radius
r and height
h. Which of the following equations correctly gives the radius of the cylinder in terms of the cylinder's volume and height?

$V=\pi r^{2} h$ $\newline$ The equation gives the Volume $V$ of a right cylinder with radius $r$ and height $h$ . Which of the following equations correctly gives the radius of the cylinder in terms of the cylinder's volume and height?

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Relate position, velocity, speed, and acceleration using derivatives

Full solution

Q.

V=\pi r^{2} h

\newline

The equation gives the Volume

V

of a right cylinder with radius

r

and height

h

. Which of the following equations correctly gives the radius of the cylinder in terms of the cylinder's volume and height?

Start with volume formula: Step $1$ : Start with the given volume formula for a cylinder, $V = \pi r^2 h$ . We need to solve for $r$ in terms of $V$ and $h$ .
Isolate $r^2$ by dividing: Step $2$ : Isolate $r^2$ by dividing both sides of the equation by $\pi h$ . So, $r^2 = \frac{V}{(\pi h)}$ .
Take square root to solve: Step $3$ : Take the square root of both sides to solve for $r$ . Thus, $r = \sqrt{\frac{V}{\pi h}}$ .

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