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The perimeter of a quarter circle is $3.57$ inches. What is the quarter circle's radius? $\newline$ Use $\pi \approx 3.14$ and round your answer to the nearest hundredth. $\newline$ ____ inches

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Circles: word problems

Full solution

Q. The perimeter of a quarter circle is

3.57

inches. What is the quarter circle's radius?

\newline

Use

\pi \approx 3.14

and round your answer to the nearest hundredth.

\newline

____ inches

Understand Problem: Step $1$ : Understand the problem and identify the formula needed. $\newline$ We need to find the radius of a quarter circle given its perimeter. The formula for the perimeter of a full circle is $P = 2\pi r$ . For a quarter circle, the perimeter includes the arc and the two radii, so the formula becomes $P = \frac{1}{2} \pi r + 2r$ .
Set Up Equation: Step $2$ : Set up the equation and solve for $r$ . $\newline$ Given $P = 3.57$ inches, we use the formula $3.57 = \frac{1}{2} \pi r + 2r$ . $\newline$ Let's simplify and solve for $r$ : $\newline$ $3.57 = 1.57r + 2r$ $\newline$ $3.57 = 3.57r$ $\newline$ $r = \frac{3.57}{3.57}$ $\newline$ $r = 1.00$ inches.

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