Question

the radius of a circle is 2 inches. what is the area of a sector bounded by a 90° arc? give the exact answer in simplest form. square inches

Explanation:

Step1: Datos dados

Radio \( r = 2 \) pulgadas, ángulo central \( \theta = 90^\circ \)

Step2: Área del círculo completo

\( A_{\text{círculo}} = \pi r^2 = \pi (2)^2 = 4\pi \) pulgadas²

Step3: Fracción del sector

\( \frac{\theta}{360^\circ} = \frac{90^\circ}{360^\circ} = \frac{1}{4} \)

Step4: Área del sector

\( A_{\text{sector}} = \frac{1}{4} \times 4\pi = \pi \) pulgadas²

Answer:

\(\pi\) square inches