The perimeter of a quarter circle is 3.57 feet. What is the quarter circle's radius? Use π ≈ 3.14 and round your answer to the nearest hundredth. ____ feet

Understand Problem: Step 1: Understand the problem and identify the formula needed. The perimeter of a quarter circle includes one-quarter of the circle's circumference plus the two radii. The formula for the circumference of a full circle is $ c = 2\pi r $. For a quarter circle, the circumference part is $ \frac{1}{4} \times 2\pi r $. Adding the two radii, the formula becomes $ \frac{1}{2}\pi r + 2r $.Set Up Equation: Step 2: Set up the equation using the given perimeter. Given perimeter $ P = 3.57 $ feet. Using the formula from Step 1, set up the equation: \[ \frac{1}{2}\pi r + 2r = 3.57 \]Substitute and Solve: Step 3: Substitute the value of $ \pi $ and solve for $ r $. \[ \frac{1}{2} \times 3.14 \times r + 2r = 3.57 \] \[ 1.57r + 2r = 3.57 \] \[ 3.57r = 3.57 \] \[ r = 1 \]

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

View step-by-step help

Home

Math Problems

Grade 7

Circles: word problems

Full solution

Q. The perimeter of a quarter circle is

3.57

feet. What is the quarter circle's radius?

\newline

\newline

Use

\pi \approx 3.14

and round your answer to the nearest hundredth.

\newline

____ feet

Understand Problem: Step $1$ : Understand the problem and identify the formula needed. $\newline$ The perimeter of a quarter circle includes one-quarter of the circle's circumference plus the two radii. The formula for the circumference of a full circle is $c = 2\pi r$ . For a quarter circle, the circumference part is $\frac{1}{4} \times 2\pi r$ . Adding the two radii, the formula becomes $\frac{1}{2}\pi r + 2r$ .
Set Up Equation: Step $2$ : Set up the equation using the given perimeter. $\newline$ Given perimeter $P = 3.57$ feet. $\newline$ Using the formula from Step $1$ , set up the equation: $\newline$ $\frac{1}{2}\pi r + 2r = 3.57$
Substitute and Solve: Step $3$ : Substitute the value of $\pi$ and solve for $r$ . $\newline$ $\frac{1}{2} \times 3.14 \times r + 2r = 3.57$ $\newline$ $1.57r + 2r = 3.57$ $\newline$ $3.57r = 3.57$ $\newline$ $r = 1$