Question

The perimeter of a quarter circle is 28.917 miles. What is the quarter circle's radius?

Use 3.14 for ​.

Answer 1

the radius of the quarter circle is approximately 8.103 miles.

Explanation:

The formula for the perimeter (P) of a quarter circle is:

P = (π/2) * r + 2r

where r is the radius of the quarter circle.

We are given that the perimeter is 28.917 miles, so we can plug that in for P and simplify the equation:

28.917 = (π/2) * r + 2r

Next, we can use 3.14 for π and solve for r:

28.917 = (3.14/2) * r + 2r

28.917 = 1.57r + 2r

28.917 = 3.57r

r = 28.917/3.57

r ≈ 8.103 miles

Therefore, the radius of the quarter circle is approximately 8.103 miles.

Answer 2

8.1 miles

Explanation:

You want the radius of a quarter circle that has a perimeter of 28.917 miles.

Perimeter

The perimeter of the quarter circle is the sum of the straight segments bounding the sector, and the length of the curved segment, which is 1/4 of the circumference of the circle.

P = 2r +1/4(2πr) = r(π/2 +2)

28.917 = r(3.14/2 +2) = 3.57r

r = 28.917/3.57 = 8.1 . . . . . miles

The quarter circle's radius is 8.1 miles.

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