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

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Circles: word problems

Full solution

Q. The perimeter of a quarter circle is

3.57

yards. What is the quarter circle's radius?

\newline

\newline

Use

\pi \approx 3.14

and round your answer to the nearest hundredth.

\newline

____ yards

Understand Formula: First, we need to understand the formula for the perimeter of a quarter circle. The perimeter $P$ of a quarter circle includes one-quarter of the circle's circumference plus the two radius lengths. The formula is $P = (\pi * r) / 2 + 2r$ .
Substitute and Solve: Next, we substitute the given perimeter and the approximate value of $\pi$ into the formula and solve for $r$ . We have $3.57 = (3.14 \times r) / 2 + 2r$ .
Combine Terms and Solve: Combine like terms and solve for $r$ . First, multiply through by $2$ to clear the fraction: $2 \times 3.57 = 3.14r + 4r$ , $7.14 = 7.14r$ , $r = 7.14 / 7.14$ , $r = 1$ .

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\newline

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Question

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\newline

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\newline

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Question

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\newline

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\newline

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