Answers to homework problems – page 8

Areas of Circles and Sectors

Theorem 11.7 Area of a Circle

The area of a circle is

€

π times the square of the radius,

or A = πr2

Theorem 11.8 Area of a Sector

The ratios of the area A of a sector of a circle to the area of the circle is equal to the ratio of the measure of the intercepted arc to 360∘.

€

A

πr2 =mAB

360o , or A =mAB

360o • πr2

Find the area of the blue shaded region.

€

1. 12π in 2. (100 - 25π ) cm2 3. (64π - 8) ft 2

Find the area of the yellow ring.

€

27π

Find the area of the circular sector whose chord is the side of the square inscribed in a circle

with a 4 cm radius.

Calculate the area of a circular sector whose chord is the side of

an inscribed equilateral triangle in a circle with a 2 cm radius.