Answer:
Area = 48π
Step-by-step explanation:
Area of the Sector
[tex]\text{area of sector} = \pi r^2 \times \frac{\text{angle in degrees}}{360^\circ}[/tex]
r ... radius
Given:
diameter = 24
angle = 120°
Radius is half the diameter.
r = 12
Insert values in the formula.
[tex]\text{A} = \pi r^2 \times \frac{\text{angle in degrees}}{360^\circ}[/tex]
[tex]\text{A} = \pi (12)^2 \times \frac{(120)^\circ}{360^\circ}[/tex]
And calculate. But do not multiply with pi. Only multiply numbers.
[tex]\text{A} = \pi \times 144 \times \frac{1}{3}[/tex]
[tex]\text{A} = \pi 48[/tex]
[tex]\text{A} = 48 \pi[/tex]
