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The perimeter of a quarter circle is $17.85$ feet. What is the quarter circle's radius? $\newline$ Use $\pi \approx 3.14$ and round your answer to the nearest hundredth. $\newline$ ____ feet

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Volume of cylinders

Full solution

Q. The perimeter of a quarter circle is

17.85

feet. What is the quarter circle's radius?

\newline

Use

\pi \approx 3.14

and round your answer to the nearest hundredth.

\newline

____ feet

Identify Formula: Identify the formula for the perimeter of a quarter circle, which includes the curved part and two radius lines. The formula for the perimeter of a full circle is $2\pi r$ , so for a quarter circle, it's $\frac{1}{4}(2\pi r) + 2r$ .
Set Up Equation: Set up the equation with the given perimeter: $\newline$ $\frac{1}{4}(2\pi r) + 2r = 17.85$ $\newline$ Simplify and solve for $r$ : $\newline$ $\frac{1}{2}\pi r + 2r = 17.85$ $\newline$ Use $\pi \approx 3.14$ : $\newline$ $1.57r + 2r = 17.85$ $\newline$ Combine like terms: $\newline$ $3.57r = 17.85$ $\newline$ Divide both sides by $3$ . $57$ : $\newline$ $r = \frac{17.85}{3.57}$ $\newline$ Calculate: $\newline$ $r \approx 5.00$

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