The radius of a quarter circle is 1 meter. What is the quarter circle's perimeter? Use π ≈ 3.14 and round your answer to the nearest hundredth. ____ meters

Identify Formula: Step 1: Identify the formula for the perimeter of a quarter circle. The perimeter includes the curved part (quarter of the total circumference) plus the two radii. Formula for the circumference of a full circle is $ c = 2\pi r $. For a quarter circle, the curved part is $ \frac{1}{4} \times 2\pi r $. Calculate Curved Part: Step 2: Plug in the radius value and calculate the curved part of the perimeter. Given $ r = 1 $ meter and $ \pi \approx 3.14 $, Curved part = $ \frac{1}{4} \times 2 \times 3.14 \times 1 = 1.57 $ meters. Find Total Perimeter: Step 3: Add the lengths of the two radii to the curved part to find the total perimeter. Each radius is 1 meter, so the total from the radii is $ 1 + 1 = 2 $ meters. Total perimeter = Curved part + 2 radii = $ 1.57 + 2 = 3.57 $ meters.

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The radius of a quarter circle is $1\,\text{meter}$ . What is the quarter circle's perimeter? $\newline$ Use $\pi \approx 3.14$ and round your answer to the nearest hundredth. $\newline$ $\_\_\_\_$ meters

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Grade 7

Circles: word problems

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Q. The radius of a quarter circle is

1\,\text{meter}

. What is the quarter circle's perimeter?

\newline

Use

\pi \approx 3.14

and round your answer to the nearest hundredth.

\newline

\_\_\_\_

meters

Identify Formula: Step $1$ : Identify the formula for the perimeter of a quarter circle. The perimeter includes the curved part (quarter of the total circumference) plus the two radii. Formula for the circumference of a full circle is $c = 2\pi r$ . For a quarter circle, the curved part is $\frac{1}{4} \times 2\pi r$ .
Calculate Curved Part: Step $2$ : Plug in the radius value and calculate the curved part of the perimeter. Given $r = 1$ meter and $\pi \approx 3.14$ , $\newline$ Curved part = $\frac{1}{4} \times 2 \times 3.14 \times 1 = 1.57$ meters.
Find Total Perimeter: Step $3$ : Add the lengths of the two radii to the curved part to find the total perimeter. Each radius is $1$ meter, so the total from the radii is $1 + 1 = 2$ meters. $\newline$ Total perimeter = Curved part + $2$ radii = $1.57 + 2 = 3.57$ meters.