The area of a sector is \(18\pi \text{cm}^2\), and its radius is 6 cm. What is the central angle (in radians)?
The area of a sector is \(18\pi \text{cm}^2\), and its radius is 6 cm. What is the central angle (in radians)?
किसी वृत्तीय खंड (sector) का क्षेत्रफल $18\pi \text{ सेमी}^2$ है और उसकी त्रिज्या 6 सेमी है। केंद्रीय कोण (रेडियन में) ज्ञात कीजिए।
Detailed Solution & Logic
Correct Answer:
\(\pi\)
Solution:
Area of a sector (in radians)
$A = \frac{1}{2} r^2 \theta$
Given,
$A = 18\pi$, $r = 6$
So,
$18\pi = \frac{1}{2} \times 6^2 \times \theta$
$18\pi = \frac{1}{2} \times 36 \times \theta$
$18\pi = 18\theta$
$\theta = \pi$
Answer: The central angle is $\pi$ radians.
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