Question

the diameter of a circle is 30 feet. what is the area of a sector bounded by a 40° arc? give the exact answer in simplest form. square feet

Explanation:

Step1: Calculate radius

$r = \frac{d}{2} = \frac{30}{2} = 15$ ft

Step2: Sector area formula

$Area = \frac{\theta}{360^\circ} \times \pi r^2$

Step3: Substitute values

$Area = \frac{40^\circ}{360^\circ} \times \pi \times 15^2 = \frac{1}{9} \times 225\pi = 25\pi$

Answer:

25π square feet