Question

a string is laid on the ground in the shape of a rectangle with length 13 inches and width 7 inches. if the string is then reformed into the shape of a circle, find the area of the circle to the nearest hundredth of a square inch. 125.03 126.19 127.32 123.96 122.81

Explanation:

Step1: Find the perimeter of the rectangle

The perimeter of a rectangle is given by $P = 2(l + w)$. Here, $l = 13$ inches and $w = 7$ inches. So $P=2(13 + 7)=2\times20 = 40$ inches. This perimeter is equal to the circumference of the circle formed later.

Step2: Find the radius of the circle

The circumference of a circle is $C = 2\pi r$. Since $C = 40$ inches, we have $2\pi r=40$. Solving for $r$, we get $r=\frac{40}{2\pi}=\frac{20}{\pi}$ inches.

Step3: Find the area of the circle

The area of a circle is $A=\pi r^{2}$. Substituting $r = \frac{20}{\pi}$ into the formula, we have $A=\pi(\frac{20}{\pi})^{2}=\pi\times\frac{400}{\pi^{2}}=\frac{400}{\pi}\approx\frac{400}{3.14159}\approx127.32$ square - inches.

Answer:

127.32