The perimeter of a quarter circle is 10.71 meters. What is the quarter circle's radius? Use π ≈ 3.14 and round your answer to the nearest hundredth. ____ meters

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 full circle's circumference is $2\pi r$, so for a quarter circle, the curved part is $\frac{1}{4} \times 2\pi r = \frac{\pi r}{2}$. Adding two radius lines, the total perimeter $P$ is $\frac{\pi r}{2} + 2r$.Set Up Equation: Set up the equation with the given perimeter: \[ \frac{\pi r}{2} + 2r = 10.71 \] Substitute $\pi \approx 3.14$ into the equation: \[ \frac{3.14r}{2} + 2r = 10.71 \]Combine Like Terms: Combine like terms: \[ \frac{3.14r}{2} + 2r = 10.71 \] \[ \left(\frac{3.14}{2} + 2\right)r = 10.71 \] \[ (1.57 + 2)r = 10.71 \] \[ 3.57r = 10.71 \]Solve for r: Solve for $r$: \[ r = \frac{10.71}{3.57} \] \[ r \approx 3.00 \] meters

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The perimeter of a quarter circle is $10.71$ meters. What is the quarter circle's radius? $\newline$ $\newline$ Use $\pi \approx 3.14$ and round your answer to the nearest hundredth. $\newline$ ____ meters

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Q. The perimeter of a quarter circle is

10.71

meters. What is the quarter circle's radius?

\newline

\newline

Use

\pi \approx 3.14

and round your answer to the nearest hundredth.

\newline

____ meters

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 full circle's circumference is $2\pi r$ , so for a quarter circle, the curved part is $\frac{1}{4} \times 2\pi r = \frac{\pi r}{2}$ . Adding two radius lines, the total perimeter $P$ is $\frac{\pi r}{2} + 2r$ .
Set Up Equation: Set up the equation with the given perimeter: $\newline$ $\frac{\pi r}{2} + 2r = 10.71$ $\newline$ Substitute $\pi \approx 3.14$ into the equation: $\newline$ $\frac{3.14r}{2} + 2r = 10.71$
Combine Like Terms: Combine like terms: $\newline$ $\frac{3.14r}{2} + 2r = 10.71$ $\newline$ $\left(\frac{3.14}{2} + 2\right)r = 10.71$ $\newline$ $(1.57 + 2)r = 10.71$ $\newline$ $3.57r = 10.71$
Solve for r: Solve for $r$ : $\newline$ $r = \frac{10.71}{3.57}$ $\newline$ $r \approx 3.00$ meters