As shown in the diagram,overline{OA} and over | vedclass

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

Question

(A) For the sector $OACB$,the radius $r = 35 	ext{ cm}$ and the measure of the angle $	heta = 90^{\circ}$ (since $\overline{OA} \perp \overline{OB}$

Vedclass · Accepted Answer

$752.5$

Vedclass · Answer

(A) For the sector $OACB$,the radius $r = 35 	ext{ cm}$ and the measure of the angle $	heta = 90^{\circ}$ (since $\overline{OA} \perp \overline{OB}$).Area of sector $OACB = \frac{\pi r^2 	heta}{360^{\circ}}$$= \frac{22}{7} 	imes \frac{35 	imes 35 	imes 90^{\circ}}{360^{\circ}}$$= 962.5 	ext{ cm}^2$In $\Delta ODA$,$\angle O = 90^{\circ}$.Area of $\Delta ODA = \frac{1}{2} 	imes OD 	imes OA$$= \frac{1}{2} 	imes 12 	imes 35$$= 210 	ext{ cm}^2$Area of the shaded region = Area of sector $OACB - 	ext{Area of } \Delta ODA$$= 962.5 - 210$$= 752.5 	ext{ cm}^2$Thus,the area of the shaded region is $752.5 	ext{ cm}^2$.

As shown in the diagram,$\overline{OA}$ and $\overline{OB}$ are two radii of $\odot(O, 35 \text{ cm})$ perpendicular to each other. If $OD = 12 \text{ cm}$,find the area of the shaded region. (in $\text{cm}^2$)

Similar Questions

In a circle with radius $21 \ cm$,the perimeter of a minor sector is $64 \ cm$. Then,the length of the arc of that sector is $\ldots \ cm$.

In a circle with radius $42\,cm$,an arc subtends an angle of measure $120^{\circ}$ at the centre. Then,the area of the minor sector formed by that arc is $\ldots \ldots \ldots \,cm^{2}$.

In $\odot(O, 4)$,$\widehat{ACB}$ is a minor arc and $m \angle AOB = 45^\circ$. Then,the length of minor $\widehat{ACB}$ is $\ldots \ldots \ldots \ldots$

In a circle with radius $21 \, cm$,the length of a minor arc is $33 \, cm$. Find the measure of the angle subtended at the centre by this arc. Also,find the area of the minor sector and the area of the minor segment formed by it.

In a circle with radius $42 \ cm$,a minor arc subtends an angle of $60^{\circ}$ at the centre. Find the area of the minor sector and the minor segment corresponding to this arc. (Use $\sqrt{3} = 1.73$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module