Find the area of the segment of a circle of radius $12 \, cm$ whose corresponding sector has a central angle of $60^{\circ}$ (Use $\pi = 3.14$).

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Given that,radius of a circle $(r) = 12 \, cm$ and central angle of sector $(\theta) = 60^{\circ}$.
Area of sector $= \frac{\pi r^2 \theta}{360^{\circ}} = \frac{3.14 \times 12 \times 12 \times 60^{\circ}}{360^{\circ}} = 3.14 \times 2 \times 12 = 75.36 \, cm^2$.
Since the triangle formed by the two radii and the chord is an isosceles triangle with a vertex angle of $60^{\circ}$,it is an equilateral triangle.
Area of equilateral triangle $= \frac{\sqrt{3}}{4} \times (\text{side})^2 = \frac{\sqrt{3}}{4} \times 12^2 = 36\sqrt{3} \, cm^2$.
Area of the segment $=$ Area of sector $-$ Area of triangle $= (75.36 - 36\sqrt{3}) \, cm^2$.

Explore More

Similar Questions

In $\odot(O, 6)$, $\widehat{ABC}$ is a major arc and $m \angle AOC = 60^{\circ}$. Then, the length of major $\widehat{ABC}$ is ........... (in $\pi$)

In the adjoining figure,$PS$ is the diameter of a circle and $PS = 12$. $PQ = QR = RS$. Semicircles are drawn with diameters $\overline{PQ}$ and $\overline{QS}$. Find the perimeter and the area of the shaded region. $(\pi = 3.14)$

Difficult
View Solution

Three circles each of radius $3.5\, cm$ are drawn in such a way that each of them touches the other two. Find the area enclosed between these circles. (in $cm^{2}$)

Difficult
View Solution

$A$ wire fence is to be put up all around a circular ground with diameter $105 \, m$. The length of the fence is $\ldots \ldots \ldots \ldots \, m$.

Is it true that the distance travelled by a circular wheel of diameter $d \text{ cm}$ in one revolution is $2 \pi d \text{ cm}$? Why?

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo