Question

the radius of a circle is 4 meters. what is the area of a sector bounded by a 135° arc? give the exact answer in simplest form. square meters

Explanation:

Step1: Use sector area formula

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

Step2: Substitute values

$\theta=135^\circ$, $r=4$, so $A = \frac{135}{360} \times \pi \times 4^2$

Step3: Simplify fraction

$\frac{135}{360} = \frac{3}{8}$

Step4: Calculate $4^2$

$4^2 = 16$

Step5: Compute result

$A = \frac{3}{8} \times \pi \times 16 = 6\pi$

Answer:

$6\pi$