Question

the diameter of a circle is 2 feet. what is the area of a sector bounded by a 78° arc? give the exact answer in simplest form. square feet

Explanation:

Step1: Calculate radius

Radius \( r = \frac{d}{2} = \frac{2}{2} = 1 \) ft

Step2: Area of full circle

\( \text{Area} = \pi r^2 = \pi (1)^2 = \pi \) sq ft

Step3: Sector area fraction

\( \text{Fraction} = \frac{78^\circ}{360^\circ} = \frac{13}{60} \)

Step4: Sector area

\( \text{Sector area} = \frac{13}{60} \times \pi = \frac{13\pi}{60} \) sq ft

Answer:

\(\frac{13\pi}{60}\) square feet