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

All the vertices of a rhombus lie on a circle. Find the area of the rhombus,if the area of the circle is $1256 \, cm^{2}$. (Use $\pi = 3.14$). (in $cm^{2}$)

The diameter of a circle with area $38.5 \, m^2$ is $\ldots \ldots \ldots \ldots m$.

In $\odot(O, 12)$, minor $\widehat{ACB}$ subtends an angle of measure $30^{\circ}$ at the centre. Then, the length of major $\widehat{ADB}$ is $\ldots \ldots \ldots \text{ cm}$. (in $\pi$)

In a circle with radius $6 \, cm$,a minor arc subtends an angle of measure $60^{\circ}$ at the centre. Find the area of the minor sector and the major sector corresponding to that arc.

It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters $16 \, m$ and $12 \, m$ in a locality. The radius of the new park would be (in $m$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module