The area of a circle A is 85π ft2. ∠BAC is a central angle of the circle, and m∠BAC = 36°

What is the area of the 36° sector?

Question 1 options:

8.5πft2

10πft2

17πft2

21.25πft2

As stated the area of the circle is 85π ft2. The area of the sector BAC is a portion of this full circle area. the sector is made of 2 radii and arc that has rotated by 36°.

the magnitude of the central angle in the circle is 360°

Area for 360° central angle - 85π ft2

then the area for 1° = 85π ft2/360°

the area of 36° sector = 85π ft2/360° x 36°

= 8.5π ft2