Is it true to say that the area of a segment of a circle is less than the area of its corresponding sector? Why?
(B) The statement is false.
$1$. $A$ segment of a circle is the region bounded by a chord and an arc. $A$ sector of a circle is the region bounded by two radii and an arc.
$2$. For a minor segment,the area is indeed less than the area of the corresponding minor sector because the minor segment is a part of the minor sector (the sector includes the triangle formed by the two radii and the chord).
$3$. However,for a major segment,the area is always greater than the area of the corresponding major sector. Therefore,the statement is not universally true.
$1$. $A$ segment of a circle is the region bounded by a chord and an arc. $A$ sector of a circle is the region bounded by two radii and an arc.
$2$. For a minor segment,the area is indeed less than the area of the corresponding minor sector because the minor segment is a part of the minor sector (the sector includes the triangle formed by the two radii and the chord).
$3$. However,for a major segment,the area is always greater than the area of the corresponding major sector. Therefore,the statement is not universally true.
Explore More
Similar Questions
In a circle with radius $14 \, cm$,$\overline{OA}$ and $\overline{OB}$ are radii perpendicular to each other. Then,the area of the minor sector corresponding to $\angle AOB$ is $\ldots \ldots \ldots \, cm^2$.
Medium
View SolutionPoints $A$ and $B$ are distinct points on $\odot(O, r)$ and point $C$ on the circle lies in the interior of $\angle AOB$. Then,$\overline{AB} \cup \widehat{ACB}$ is ........
Medium
View SolutionThe length of a square field is $50 \, m$. $A$ cow is tethered at one of the vertices by a $3 \, m$ long rope. Find the area of the region of the field in which the cow can graze. $(\pi = 3.14)$ (in $m^2$)
Medium
View SolutionIs the area of the largest circle that can be drawn inside a rectangle of length $a \, cm$ and breadth $b \, cm$ $(a > b)$ equal to $\pi b^{2} \, cm^{2}$? Why?
Easy
View SolutionIn a circle with radius $50 \, cm$,the area of the sector formed by a $20 \, cm$ long arc is $\ldots \ldots \ldots cm^2$.
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo