Question

Question 39 of 40

The circle below has a radius of 8 centimeters. What is the area of the shaded
region?
X
120°
8 cm
OA. 32 square centimeters
B. 8 square centimeters
64
3
square centimeters
square centimeters
O C.
O D.
16
3

Answer 1

Convert angle to radians

• 120=2π/3

So

Area

• r²Ø/2
• 8²(2π/3)(1/2)
• 64π/3cm²

Answer 2

`\textsf{C.} \quad (64 \pi)/(3) \: \sf square\:centimeters`

Explanation:

Formula

`\textsf{Area of a sector of a circle}=\left((\theta)/(360^(\circ))\right) \pi r^2`

`\textsf{(where r is the radius and the angle }\theta \textsf{ is measured in degrees)}`

Given:

• 
  `\theta` = 120°
• r = 8 cm

Substitute the given values into the formula and solve for Area:

`\large \begin{aligned}\implies \textsf{Area} & =\left((120^(\circ))/(360^(\circ))\right) \pi (8)^2\\\\& =\left((1)/(3)\right) \pi (64)\\\\& =(64)/(3) \pi \: \sf cm^2\end{aligned}`