Question

What is the area of the shaded sector?

Answer 1

see explanation

Explanation:

area of sector = area of circle × fraction of circle

= π × 24² ×
`(45)/(360)`

= π × 576 ×
`(1)/(8)` = 72π units² ← exact value

area of sector = 72π units² ≈ 226.2 units² ( 1 dec. place )

Answer 2

= 72*pi

If we approximate pi

= 226.08

Explanation:

The area of the entire circle is

A = pi * r^2

where r = 24

A = pi * 24^2

A = pi *576

45 degrees is part of a 360 degree circle

45/360 =1/8

Multiply the area by 1/8 since it is 1/8 of the circle

1/8 A = 1/8 * 576pi

= 72*pi

If we approximate pi

= 226.08