Question

1. if a circles sector has an area of 25π square cm and the central angle is π/2 radians, what is the radius?

a. 12 cm
b. 5 cm
c. 10 cm
d. 20 cm

Explanation:

Step1: Recall sector area formula (radians)

Sector area $A = \frac{1}{2}r^2\theta$, where $\theta$ is central angle in radians.

Step2: Substitute given values

Given $A = 25\pi$, $\theta = \frac{\pi}{2}$. Plug into formula:
$25\pi = \frac{1}{2}r^2 \cdot \frac{\pi}{2}$

Step3: Solve for $r^2$

Simplify right side: $\frac{1}{4}r^2\pi$. Cancel $\pi$ both sides:
$25 = \frac{1}{4}r^2$ → $r^2 = 100$

Step4: Find radius $r$

$r = \sqrt{100} = 10$

Answer:

c. 10 cm