Question

find the area of a circle with a circumference of 73.9 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

The formula for the circumference of a circle is $C = 2\pi r$. Given $C=73.9$, we can solve for $r$: $r=\frac{C}{2\pi}=\frac{73.9}{2\pi}$. Rounding to the nearest thousandth, $r=\frac{73.9}{2\pi}\approx11.761$.

Step2: Calculate the area of the circle

The formula for the area of a circle is $A=\pi r^{2}$. Substitute $r\approx11.761$ into the formula: $A = \pi\times(11.761)^{2}$. Calculate $A=\pi\times138.311121\approx434.6$.

Answer:

$434.6$ in²