Question

The radius of a circle is 8 miles. What is the area of a sector bounded by a 45° arc in

terms of ?
a. 64 miles
b. 4 miles
c. 8 miles
d. 512 miles

Answer 1

`8\pi\text{ mi}^2`

Explanation:

The area of a full circle is
`A = \pi r^2` where r is the radius.

The area of the circle in this problem is
`A=\pi(8)^2=64\pi`.

A 45 degree central angle (that's how arcs are measured) accounts for 1/8 of the circle (because it's 45 degrees out of a full circle of 360 degrees, and 45/360 = 1/8).

The area of the sector is
`(1)/(8)(64\pi)=8\pi` square miles