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

As shown in the diagram,$\triangle ABC$ is an equilateral triangle in which $BC = 70 \, cm$ and $P$ and $R$ are midpoints of $\overline{AB}$ and $\overline{AC}$ respectively. $\widehat{PQR}$ is an arc of $\odot(A, AP)$. Find the area of the shaded region. $(\sqrt{3} = 1.73)$ (in $cm^2$)

The radii of two concentric circles are $14 \, cm$ and $10.5 \, cm$. Then,the difference between their circumferences is $\ldots \ldots \ldots \, cm$.

Difficult
View Solution

The length of the minute hand of a clock is $6 \, cm$. The area of the region swept by it in $10 \, \text{minutes}$ is $\ldots \ldots \ldots \ldots \, cm^2$. $(\pi = 3.14)$

In a circle with radius $20\, cm$,the area of a sector formed by an arc of length $10\, cm$ is ............. $cm^2$.

Circumferences of two circles are equal. Is it necessary that their areas be equal? 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