In odot(O, r),the length of minor widehat{ACB | vedclass

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

Question

(B) The circumference of a circle is given by $C = 2\pi r$,where $r$ is the radius.The length of an arc $L$ subtending an angle $	heta$ at the centre

Vedclass · Accepted Answer

$45$

Vedclass · Answer

(B) The circumference of a circle is given by $C = 2\pi r$,where $r$ is the radius.The length of an arc $L$ subtending an angle $	heta$ at the centre is given by $L = \frac{	heta}{360^\circ} 	imes 2\pi r$.According to the problem,the length of the arc is one-eighth of the circumference:$L = \frac{1}{8} 	imes 2\pi r$.Equating the two expressions for $L$:$\frac{	heta}{360^\circ} 	imes 2\pi r = \frac{1}{8} 	imes 2\pi r$.Dividing both sides by $2\pi r$:$\frac{	heta}{360^\circ} = \frac{1}{8}$.Solving for $	heta$:$	heta = \frac{360^\circ}{8} = 45^\circ$.Thus,the measure of the angle subtended at the centre is $45^\circ$.

In $\odot(O, r)$,the length of minor $\widehat{ACB}$ is one-eighth of the circumference of the circle. Then,the measure of the angle subtended at the centre by that arc is $\ldots \ldots \ldots \ldots$ (in $^\circ$)

Similar Questions

Find the area of the sector of a circle with radius $4\, cm$ and of angle $30^{\circ}$. Also,find the area of the corresponding major sector (in $cm^2$) (Use $\pi = 3.14$).

Find the area of a sector of a circle of radius $21 \, cm$ and central angle $120^{\circ}$. (in $cm^{2}$)

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 $\ldots \ldots \ldots \ldots \, cm^2$. $(\pi = 3.14)$

Find the difference of the areas of two segments of a circle formed by a chord of length $5 \, cm$ subtending an angle of $90^{\circ}$ at the centre.

Find the area of the shaded region in the figure if $ABCD$ is a square of side $14 \, cm$ and $APD$ and $BPC$ are semicircles. (in $cm^2$) [Use $\pi = \frac{22}{7}$]

Vedclass Test Series

Exam Paper Generator

Online Exam Module