Area of Sector

Q.

How would you go about finding the area of the major sector?

1. Area of circle - Area of minor sector

2. Area of circle + Area of minor sector

3. Perimeter of the minor sector x radius

4. Perimeter of major sector x perimeter of minor sector

Q.

When the degree measure of the angle at the center is 1, what is the area of the sector with radius r = 1?

1. 

2. 180

3. 360

4. 

Q.

The radius of a circle is 7 cm and it forms a sector by rotating through 60${}^{\circ }$. Then, the radius gets doubled and further moves 30${}^{\circ }$ to form another sector. What is the area of the total region covered by the radius? ( Take π= $\frac{22}{7}$)

1. 308 cm²

2. 77 cm²

3. 154 cm²

4. 144 cm²

Q.

In a restaurant, WiFi signal has to be provided only to the deluxe class. Signal reaches each of the customer upto a distance of 21 m from the antenna and the total area for which signal to be provided is 231 $m^2$. What is the angle (in degrees) at which the signal has to be spread over a sector by the antenna?

1. 90

2. 45

3. 180

4. 60

Q. An umbrella has 8 ribs which are equally spaced. Assuming the umbrella to be a flat circle of radius 42 $cm$, find the area in $c{m}^2$ between the two consecutive ribs of the umbrella. (Take $\pi =\frac{22}{7}$)

Q. Find the area of a sector with a central angle of $120$ degrees and a radius of $10cm$

1. $20\pi c{m}^2$
2. $10\pi c{m}^2$
3. $30\pi c{m}^2$
4. $40\pi c{m}^2$

Q. If the area of the sector of a circle with angle ${45}^{\circ }$ is $11c{m}^2$ , then the area of corresponding major sector is equal to.

1. $88c{m}^2$
2. $66c{m}^2$
3. $77c{m}^2$

Q. In the figure given below, $ABCD$ is a rectangle, $AB=14cm,BC=7cm$. From the rectangle, a quarter circle $BFEC$ and a semicircle $DGE$ are removed. Calculate the area of the remaining piece of the rectangle. (Take $\pi =\frac{22}{7}$)

Q. If $16{}^n{P}_3=13{}^{n+1}{P}_3$, find $n$.

Q. If the area of the sector of a circle with angle ${45}^{\circ }$ is $11c{m}^2$ , then the area of corresponding major sector is equal to.

1. $88c{m}^2$
2. $66c{m}^2$
3. $77c{m}^2$

Q. In the figure alongside, $OAB$ is a quadrant of a circle. The radius $OA=3.5cm$ and $OD=2cm$. Calculate the area of the shaded portion. $(\text{Take}\pi =\frac{22}{7})$

Q. In the figure, $ABCD$ is a parallelogram, $P$ is a point on $AB$ produced and $DN\perp AB$.

Q. Radius of a circle with centre O is 8cm. Points A and B are such that AO= 6cm and BO =10cm state which of the points A and B is in the interior and exterior of the circle.

1. Point B is in interior and point A is in exterior of the circle.
2. Point A is in interior and point B is in interior of the circle.
3. Point A is in interior and point B is in exterior of the circle.
4. Point A is in exterior and point B is in exterior of the circle.

Q. Find the area of shaded region in each of the following figures

Q.

A car is provided with 2 non overlapping wipers. The structure of each wiper is as shown in the figure. The brown blade actually wipes the glass sweeping through an angle of ${120}^{\circ }$. If the length of the wiper is 35 cm and length of the blade is 28 cm, find the total area(in $c{m}^2$) cleaned for each sweep.

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Q. Two rods of lengths $a$ and $b$ slide along the x-axis and y-axis respectively in such a manner that their ends are concyclic. The locus of the centre of the circle passing through the end points is

1. $4(x^2+y^2)=a^2+b^2$
2. $x^2+y^2=a^2+b^2$
3. $4(x^2-y^2)=a^2-b^2$
4. $x^2-y^2=a^2-b^2$

Q. Find the area of shaded region, if in parallelogram ABCD, $\angle$PBQ=$\angle$SDR = ${60}^o$, BP=BQ=SD=RD= 21 cm, BC = 45 cm and MN = 20 cm.

Q. Area of a circle is the combined area of its major and minor sector.

1. True
2. False

Q. The longer side of a parallelogram is 54$cm$ and the corresponding altitude is 16$cm$. If the altitude corresponding to the shorter side is $24cm,$ find the length of the shorter side.

Q. In the given figure, $O$ is the centre of the circle. Given that $OD=OE=3$ cm and $AD=4$ cm. Find the length of the longest chord.

1. $6$ cm
2. $8$ cm
3. $10$ cm
4. $9$ cm