In odot(O, r),overline{OA} and overline{OB} a | vedclass

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

Question

(D) For the minor sector $OACB$,the central angle $	heta = 90^{\circ}$ and the radius is $r\,cm$.The perimeter of the minor sector $OACB$ is given by

Vedclass · Accepted Answer

$5.6$

Vedclass · Answer

(D) For the minor sector $OACB$,the central angle $	heta = 90^{\circ}$ and the radius is $r\,cm$.The perimeter of the minor sector $OACB$ is given by the sum of the two radii and the length of the arc $\widehat{ACB}$.Perimeter $= 2r + 	ext{length of arc } \widehat{ACB}$Since the length of an arc is $\frac{\pi r 	heta}{180}$,we have:$20 = 2r + \frac{\pi r 	imes 90}{180}$Using $\pi \approx \frac{22}{7}$:$20 = 2r + \frac{22}{7} 	imes \frac{r}{2}$$20 = 2r + \frac{11r}{7}$$20 = r \left( 2 + \frac{11}{7} ight)$$20 = r \left( \frac{14 + 11}{7} ight)$$20 = r \left( \frac{25}{7} ight)$$r = \frac{20 	imes 7}{25}$$r = \frac{4 	imes 7}{5} = \frac{28}{5} = 5.6\,cm$.

In $\odot(O, r)$,$\overline{OA}$ and $\overline{OB}$ are two radii perpendicular to each other. If the perimeter of the minor sector formed by these radii is $20\,cm$,then $r = \ldots\,cm$.

Similar Questions

If the circumference of a circle and the perimeter of a square are equal,then

The area of the circle that can be inscribed in a square of side $6 \, cm$ is (in $cm^2$) (in $\pi$)

The radius of a wheel of a car is $21 \, cm$. If it makes $800$ rotations per minute,find the speed of the car in $km/h$.

The ratio of radii of two circles is $2:3$ and the ratio of the angles at the centre of two minor sectors of those circles is $5:2$. Then,the ratio of the areas of those sectors is:

If the sum of the circumferences of two circles with radii $R_{1}$ and $R_{2}$ is equal to the circumference of a circle of radius $R$,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module