Question

Please answer this correctly

Answer 1

Answer:

The area of the quarter circle = 346.19 miles²

Step-by-step explanation:

If the perimeter of a quarter circle = 74.97 miles

r + r + 1/4 * 2pi*r = 74.97 miles

2r + 1/2r * pi = 74.97

Multiply left and right of the = sign by 2 gives...

2 * ( 2r + 1/2 * r * pi ) = 74.97 * 2

( 4r + 2/2* r * pi ) = 149.94

r * ( 4 + 3.14 ) = 149.94

r * ( 7.14 ) = 149.94

7.14 * r = 149.94

Divide left and right of the equal sign by 7.14

7.14 / 7.14 * r = 149.94 / 7.14

r = 149.94 / 7.14

r = 21 miles

Area full circle = r² * pi

21² * pi

441 * pi

We need to calculate a quarter part of the area of the full circle, so

1/4 * 441 * pi

110.25 * pi

110.25 * 3.14

= 346.185, which rounded to the hundreth gives.

The area of the quarter circle = 346.19 miles²

Answer 2

Answer: 346.19 miles²

Step-by-step explanation:

Perimeter (P) of the quarter circle is the curve + both sides.

Perimeter of the curve

$\dfrac{1}{4}C=\dfrac{1}{4}2\pi\cdot r\\\\\\.\quad =\dfrac{\pi \cdot r}{2}$

Perimeter of the sides

2 sides = 2r

Perimeter = curve + both sides

$74.97=\dfrac{\pi \cdot r}{2}+2r\\\\\\2(74.97)=\pi \cdot r+2(2r)\\\\\\149.94=\pi r+4r\\\\\\149.94=r(\pi +4)\\\\\\\dfrac{149.94}{\pi +4}=r$

Find the Area

$\dfrac{1}{4}A=\dfrac{1}{4}\pi\bigg(\dfrac{149.94}{\pi+4}\bigg)^2\\\\\\.\quad =\dfrac{1}{4}3.14\bigg(\dfrac{149.94}{3.14+4}\bigg)^2\\\\\\.\quad =\dfrac{1}{4}3.14(21)^2\\\\\\.\quad =\large\boxed{346.185}$