The perimeter of a quarter circle is 14.28 meters. What is the quarter circle's radius? Use π ≈ 3.14 and round your answer to the nearest hundredth. ____ meters

Understand Problem: Step 1: Understand the problem and identify what is given and what needs to be found. We know the perimeter of a quarter circle is 14.28 meters. We need to find the radius of the quarter circle.Write Formula: Step 2: Write down the formula for the perimeter of a quarter circle. The perimeter of a quarter circle includes one-quarter of the circle's circumference plus the length of the two radius lines (which form the straight edges). The formula is: Perimeter = (π * radius) / 2 + 2 * radiusSet Up Equation: Step 3: Set up the equation with the given perimeter. 14.28 = (3.14 * radius) / 2 + 2 * radiusSimplify and Solve: Step 4: Simplify and solve for the radius. Combine like terms: 14.28 = 1.57 * radius + 2 * radius 14.28 = 3.57 * radius radius = 14.28 / 3.57 radius = 4 meters

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The perimeter of a quarter circle is $14.28$ 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 $\newline$

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Grade 7

Circles: word problems

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Q. The perimeter of a quarter circle is

14.28

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

\newline

Understand Problem: Step $1$ : Understand the problem and identify what is given and what needs to be found. $\newline$ We know the perimeter of a quarter circle is $14.28$ meters. We need to find the radius of the quarter circle.
Write Formula: Step $2$ : Write down the formula for the perimeter of a quarter circle. $\newline$ The perimeter of a quarter circle includes one-quarter of the circle's circumference plus the length of the two radius lines (which form the straight edges). The formula is: $\newline$ Perimeter = $(\pi \cdot \text{radius}) / 2 + 2 \cdot \text{radius}$
Set Up Equation: Step $3$ : Set up the equation with the given perimeter. $\newline$ $14.28 = \frac{3.14 \times \text{radius}}{2} + 2 \times \text{radius}$
Simplify and Solve: Step $4$ : Simplify and solve for the radius. $\newline$ Combine like terms: $\newline$ $14.28 = 1.57 \times \text{radius} + 2 \times \text{radius}$ $\newline$ $14.28 = 3.57 \times \text{radius}$ $\newline$ $\text{radius} = \frac{14.28}{3.57}$ $\newline$ $\text{radius} = 4$ meters