In a circle with radius $11.2 \, cm$,two radii are perpendicular to each other. Find the area of the minor sector,the major sector,and the minor segment corresponding to these radii.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Given: Radius $r = 11.2 \, cm$,Central angle $\theta = 90^{\circ}$.
Area of the circle $A = \pi r^2 = \frac{22}{7} \times 11.2 \times 11.2 = 394.24 \, cm^2$.
Area of the minor sector $= \frac{\theta}{360^{\circ}} \times \pi r^2 = \frac{90}{360} \times 394.24 = \frac{1}{4} \times 394.24 = 98.56 \, cm^2$.
Area of the major sector $=$ Area of circle $-$ Area of minor sector $= 394.24 - 98.56 = 295.68 \, cm^2$.
Area of the minor segment $=$ Area of minor sector $-$ Area of $\triangle OAB = 98.56 - (\frac{1}{2} \times r^2 \times \sin 90^{\circ}) = 98.56 - (0.5 \times 11.2 \times 11.2 \times 1) = 98.56 - 62.72 = 35.84 \, cm^2$.

Explore More

Similar Questions

In a circle with radius $14 \, cm$,the area of the minor sector corresponding to minor $\widehat{ACB}$ is $77 \, cm^2$. Then,minor $\widehat{ACB}$ subtends an angle of measure $\dots$ at the centre. (in $^\circ$)

The area of a square inscribed in a circle of radius $35 \, cm$ is $\ldots \ldots \ldots \ldots cm^{2}$.

The union of a chord of a circle and its corresponding arc is called $\ldots \ldots \ldots \ldots$

In a circle with radius $14 \,cm$,an arc subtends a right angle at the centre. Find the length of this arc,the area of the minor sector,and the area of the minor segment formed by it.

The length of the minute hand of a clock is $7\,cm$. The area of the region swept by it in $20$ minutes is $\ldots \ldots \ldots \,cm^2$.

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