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
\(\pi\)
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.
Similar Practice Questions
A circle has a radius of 7 cm. Calculate
A circle has a radius of 7 cm. Calculate the length of an arc that...
Two cubes of edge 5 cm are joined to form a cuboid. Find the total surface area of the cuboid.
Two cubes of edge 5 cm are joined to form a cuboid. Find the total...
If PQ and PR are the two tangents to a circle with center O, and ∠QOR= $150^\circ$, then ∠QPR is equal to:
If PQ and PR are the two tangents to a circle with center O, and...
A right circular cone is cut into two parts of equal height by a horizontal plane.
A right circular cone is cut into two parts of equal height by a horizontal...
The value (in cm\(^3\)) of a wire of diameter 10 cm and length 56 m is: take \(\pi = \frac{22}{7}\)
The value (in cm\(^3\)) of a wire of diameter 10 cm and length 56 m...
In a regular polygon, the number of
In a regular polygon, the number of diagonals is 9. Find the difference between one...
A chord of length 24 cm subtends a right angle at the center of the circle. What is the radius of the circle?
A chord of length 24 cm subtends a right angle at the center of the...