Question

find the area of a circle with a circumference of 74.6 in. use the $pi$ key for $pi$. the area of the circle is approximately (round the final answer to the nearest tenth as needed. round all intermediate values to the nearest thousandth as needed )

Explanation:

Step1: Find the radius from the circumference formula.

The formula for the circumference of a circle is $C = 2\pi r$. Given $C=74.6$ inches, we can solve for $r$:
$r=\frac{C}{2\pi}=\frac{74.6}{2\pi}$.
Calculating $\frac{74.6}{2\pi}\approx\frac{74.6}{2\times3.14159}\approx11.873$ (rounded to the nearest thousandth).

Step2: Calculate the area of the circle.

The formula for the area of a circle is $A=\pi r^{2}$. Substitute $r\approx11.873$ into the formula:
$A=\pi\times(11.873)^{2}\approx\pi\times141.007\approx442.8$ (rounded to the nearest tenth).

Answer:

$442.8$ in²