The angle of a sector is $\frac{\pi}{4}$ radians, and the radius of the circle is 8 cm. What is the area of the sector?
The angle of a sector is $\frac{\pi}{4}$ radians, and the radius of the circle is 8 cm. What is the area of the sector?
एक सेक्टर का कोण है $\frac{\pi}{4} रेडियन है, $ और वृत की त्रिज्या 8 सेमी है। त्रिज्यखंड का क्षेत्रफल क्या है?
Detailed Solution & Logic
Correct Answer:
$8 \pi {cm}^2$
Given:
Angle = $\frac{\pi}{4}$ radians
Radius = 8 cm
Area of sector
$= \frac{1}{2} r^2 \theta$
$= \frac{1}{2} \times (8)^2 \times \frac{\pi}{4}$
$= \frac{1}{2} \times 64 \times \frac{\pi}{4}$
$= 32 \times \frac{\pi}{4}$
$= 8\pi$
Final Answer: $8\pi \text{ cm}^2$ ✅
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