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Find the radius or height. Use 3.14 for pi and round your answers to the nearest hundredth where necessary.
Find the radius of a cylinder with a volume of 950in^(3) and a height of 10in.
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Find the radius or height. Use $3$ . $14$ for $\pi$ and round your answers to the nearest hundredth where necessary. $\newline$ Find the radius of a cylinder with a volume of $950 \mathrm{in}^{3}$ and a height of $10 \mathrm{in}$ . $\newline$ $\square$

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Volume of cylinders

Full solution

Q. Find the radius or height. Use

3

.

14

for

\pi

and round your answers to the nearest hundredth where necessary.

\newline

Find the radius of a cylinder with a volume of

950 \mathrm{in}^{3}

and a height of

10 \mathrm{in}

.

\newline

\square

Identify Formula and Values: Identify the formula for the volume of a cylinder and the given values. $\newline$ The formula for the volume of a cylinder is $V = \pi r^2 h$ , where $V$ is the volume, $r$ is the radius, and $h$ is the height. We are given the volume $V = 950 \, \text{in}^3$ and the height $h = 10 \, \text{in}$ .
Plug Known Values and Solve: Plug the known values into the volume formula and solve for the radius $r$ . We have $950 = \pi r^2(10)$ . To find $r$ , we need to divide both sides of the equation by $\pi$ and then by the height ( $10$ in).
Perform Division to Isolate $r^2$ : Perform the division to isolate $r^2$ . $\newline$ $\frac{950}{(\pi \cdot 10)} = r^2$ $\newline$ Using $3.14$ for $\pi$ , we get: $\newline$ $\frac{950}{(3.14 \cdot 10)} = r^2$ $\newline$ $\frac{950}{31.4} = r^2$
Calculate $r^2$ : Calculate the value of $r^2$ . $\frac{950}{31.4} = r^2$ $r^2 \approx 30.25477707$
Take Square Root to Solve for $r$ : Take the square root of both sides to solve for $r$ . $r = \sqrt{30.25477707}$ $r \approx 5.50 \text{ in} \text{ (rounded to the nearest hundredth)}$

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