Question

What circular area is covered by the signal if the circumference is 754 miles?

Answer 1

45219.4 square miles

Explanation:

Circumference of a circle is given by

`C=2\pi r`

Where r is the radius and C is circumference

Making r the subject of the formula then

`r=\frac {C}{2\pi}`

Substituting C with 754 miles then

`r=\frac {754}{2\pi}=119.95454545454miles\\r\approx 119.95 miles`

Area of a circle is given by

`A=\pi r^(2)`

Substituting 119.95miles for r then

`A=\pi 119.95^(2)=45219.436428571 mile^(2)\\A\approx 45219.4 mile^(2)`

The area is approximately 45219.4 square miles