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The radius of a quarter circle is $4\,\text{meters}$ . 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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Circles: word problems

Full solution

Q. The radius of a quarter circle is

4\,\text{meters}

. 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 for perimeter: 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 radius lines. The formula for the circumference of a full circle is $c = 2\pi r$ . For a quarter circle, the curved part is $\frac{1}{4} \times 2\pi r$ . Adding the two radii, the formula becomes $\frac{1}{2}\pi r + 2r$ .
Plug in values: Step $2$ : Plug in the values into the formula. Given $r = 4$ meters and $\pi \approx 3.14$ , substitute these into the formula: $\newline$ $\text{Perimeter} = \frac{1}{2} \times 3.14 \times 4 + 2 \times 4$ $\newline$ $\text{Perimeter} = 6.28 + 8$ $\newline$ $\text{Perimeter} = 14.28$ meters.

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