Question

Help please show work

Answer 1

This exercise is asking for the area of a circle with a given circumference. The plan of action is the following:

1. Derive the radius from the circumference
2. Use the radius to compute the area.

The first step is

$C = 2\pi r \iff r = \dfrac{C}{2\pi}$

The second step is

$A = \pi r^2 = \pi \dfrac{C^2}{4\pi^2} = \dfrac{C^2}{4\pi}$

So, the area is

$\dfrac{870^2}{4\pi} = \dfrac{756900}{4\pi} \approx 60232$