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The volume of a cylinder is 54 pi cubic inches and the height is 6 inches. Find the radius.
(A) 3cm
(B) 9cm
(C) 3.14cm
(D) 1cm

The volume of a cylinder is $54 \pi$ cubic inches and the height is $6$ inches. Find the radius. $\newline$ (A) $3 \mathrm{~cm}$ $\newline$ (B) $9 \mathrm{~cm}$ $\newline$ (C) $3.14 \mathrm{~cm}$ $\newline$ (D) $1 \mathrm{~cm}$

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. The volume of a cylinder is

54 \pi

cubic inches and the height is

6

inches. Find the radius.

\newline

(A)

3 \mathrm{~cm}

\newline

(B)

9 \mathrm{~cm}

\newline

(C)

3.14 \mathrm{~cm}

\newline

(D)

1 \mathrm{~cm}

Write Given Information: Write down the given information and the formula for the volume of a cylinder. $\newline$ The volume of a cylinder $V$ is given by the formula $V = \pi r^2 h$ , where $r$ is the radius and $h$ is the height. $\newline$ Given: $V = 54\pi$ cubic inches, $h = 6$ inches. $\newline$ We need to find the radius $r$ .
Substitute and Solve for r: Substitute the given values into the volume formula and solve for r. $\newline$ $54\pi = \pi r^2 \times 6$ $\newline$ To find $r$ , we first divide both sides of the equation by $\pi$ to eliminate $\pi$ from the equation. $\newline$ $54 = r^2 \times 6$
Isolate $r^2$ : Divide both sides of the equation by $6$ to isolate $r^2$ . $\newline$ $\frac{54}{6} = r^2$ $\newline$ $9 = r^2$
Solve for r: Take the square root of both sides to solve for r. $\newline$ $\sqrt{9} = r$ $\newline$ $3 = r$

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