Question

The radius of circle is 15 miles. What is the area of a sector bounded by a 70o arc?

Answer 1

If the area of the sector is bounded by a 70° arc then that is also the measure of the central angle in question. The formula for the area of a sector is
`A_(s) = ( \beta )/(360) * \pi r^(2)`. We now have our angle beta and we were given the radius, so filling in accordingly, we have
`A_(s) = (70)/(360) * \pi (15) ^(2)` which simplifies to
`(175 \pi )/(4)`. If you have to leave your answer in terms of pi, then you're done. If you have to multiply in the value for pi, you would have 137.44 miles squared.