Question

the diameter of a circle is 20 feet. what is the area of a sector bounded by a 144° arc? give the exact answer in simplest form. square feet

Explanation:

Step1: Calculate radius

$r = \frac{d}{2} = \frac{20}{2} = 10$ ft

Step2: Area of full circle

$A_{\text{círculo}} = \pi r^2 = \pi (10)^2 = 100\pi$ ft²

Step3: Sector angle fraction

$\text{Fracción} = \frac{144^\circ}{360^\circ} = \frac{2}{5}$

Step4: Sector area

$A_{\text{sector}} = 100\pi \times \frac{2}{5} = 40\pi$ ft²

Answer:

40π square feet