(A) The length of an arc subtending an angle $\theta$ at the centre is given by $L = \frac{\theta}{360^{\circ}} \times 2\pi r$.The circumference of th

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(A) The length of an arc subtending an angle $\theta$ at the centre is given by $L = \frac{\theta}{360^{\circ}} \times 2\pi r$.The circumference of the circle is $C = 2\pi r$.Therefore,the ratio of the length of the minor arc $\widehat{ACB}$ to the circumference is $\frac{L}{C} = \frac{(\frac{\theta}{360^{\circ}}) \times 2\pi r}{2\pi r} = \frac{\theta}{360^{\circ}}$.Given $\theta = 72^{\circ}$,the ratio is $\frac{72^{\circ}}{360^{\circ}} = \frac{1}{5}$.Thus,the ratio is $1:5$.

Class 10 Mathematics Areas Related to Circles Mix Examples - Areas Related to Circles

Easy

In $\odot(O, r)$,minor $\widehat{ACB}$ subtends an angle of measure $72^{\circ}$ at the centre. Then,the ratio of the length of minor $\widehat{ACB}$ and the circumference of the circle is ............

A
$1:5$
B
$1:6$
C
$1:8$
D
$1:9$

Explore More

Browse All

Question Bank

All Subjects

Class 10 Questions

Class 10

Mathematics Questions

Chapter

Areas Related to Circles

Subtopic

Mix Examples - Areas Related to Circles

The length of the minute hand of a clock is $10.5 \, cm$. The area of the region swept by it in $20$ minutes is $\ldots \, cm^2$.

Medium

View Solution

If the radius of a circle is increased by $10 \%,$ its area will increase by $\ldots \ldots \ldots . \%$

Medium

View Solution

In a circle with radius $r,$ an arc subtends an angle of measure $\theta$ at the centre. Then,the area of the major sector is $=$ ..........

Medium

View Solution

As shown in the diagram,$\overline{ OA }$ and $\overline{ OB }$ are two radii of $\odot( O , 21 \text{ cm} )$ perpendicular to each other. If $OD = 10 \text{ cm}$,find the area of the shaded region. (in $\text{cm}^2$)

Difficult

View Solution

The 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 Solution

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

In $\odot(O, r)$,minor $\widehat{ACB}$ subtends an angle of measure $72^{\circ}$ at the centre. Then,the ratio of the length of minor $\widehat{ACB}$ and the circumference of the circle is ............

Similar Questions

The length of the minute hand of a clock is $10.5 \, cm$. The area of the region swept by it in $20$ minutes is $\ldots \, cm^2$.

If the radius of a circle is increased by $10 \%,$ its area will increase by $\ldots \ldots \ldots . \%$

In a circle with radius $r,$ an arc subtends an angle of measure $\theta$ at the centre. Then,the area of the major sector is $=$ ..........

As shown in the diagram,$\overline{ OA }$ and $\overline{ OB }$ are two radii of $\odot( O , 21 \text{ cm} )$ perpendicular to each other. If $OD = 10 \text{ cm}$,find the area of the shaded region. (in $\text{cm}^2$)

The 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 $m^2$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module