Find Sector Area with Radius 8 cm and Central Angle π/4 Radians

Question

If the radius of the circle sector is 8 cm and its central angle $\frac{\pi}{4}$ then what its area?

Accepted Answer

$8\pi$ cm²

Answer

Step 1: Recall the formula for the area of a sector in radians: $A = \frac{1}{2}r^2\theta$, where $A$ is sector area, $r$ is radius, and $\theta$ is the central angle in radians. Step 2: Substitute the given values $r=8$ cm and $\theta=\frac{\pi}{4}$ into the formula: $A = \frac{1}{2} \times 8^2 \times \frac{\pi}{4}$. Step 3: Calculate the value: $A = \frac{1}{2} \times 64 \times \frac{\pi}{4} = 32 \times \frac{\pi}{4} = 8\pi$ cm².