Length of Arc & Angle at the Centre

Q.

In figure, ABCD is a trapezium with $AB\parallel DC$. AB = 18 cm, DC = 32 cm and distance between AB and DC = 14 cm. Arcs of equal radii 7 cm with centres A, B, C and D have been drawn , then find the area of the shaded region in the figure.

1. $148c{m}^2$

2. $196c{m}^2$

3. $126c{m}^2$

4. $121c{m}^2$

Q.

The radius of the circle given above is 7cm and the angle subtended by the arc is ${60}^{\circ }$. If the area of $\Delta$OAB is $21{cm}^2$, then the area of segment APB is___ .(Take the value of $\pi$ as $\frac{22}{7}$)

1. $5.8{cm}^2$
2. $4.7{cm}^2$
3. $1{cm}^2$
4. $8{cm}^2$

Q. If the radius of the circle is 6cm and $\theta$ is ${30}^{\circ }$, then the length of the arc of the circle is .

1. 32
2. 31.4
3. 3.14
4. 31

Q.

Question 8 (i)
Fig. 12.26 depicts a racing track whose left and right ends are semi-circular.
The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find:
(i) The distance around the track along its inner edge

Q.

Four circular cardboard pieces of radii 7 cm are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces.

1. $42c{m}^2$

2. $48c{m}^2$.

3. $22c{m}^2$.

4. $38c{m}^2$.

Q.

An archery target has three regions formed by three concentric circles as shown in figure. If the diameters of the concentric circles are in the ratio 1:2:3, then find the ratio of the areas of three regions.

1. 1:9:4

2. 2:5:8

3. 1:2:3

4. 1:3:5

Q.

Find the difference of the areas of a sector of angle ${120}^{\circ }$ and its corresponding major sector of a circle of radius 21 cm.

1. $162c{m}^2$

2. $412c{m}^2$

3. $382c{m}^2$

4. $462c{m}^2$

Q.

Find the area of the shaded region from the figure given below:

1. 46.5 sq. cm

2. 46 sq. cm

3. 50 sq. cm

4. 48 sq. cm

Q.

Are the areas of unshaded regions in the two figures equal?

1. The radius of the quarter circles in figure 1 is equal to the radius of the circle in figure 2

2. Both A and B

3. None of the above

4. The radii of the quarter circles are equal.
   

Q. In Fig. 7, OABC is a rectangle inscribed in a quadrant of a circle of radius 25 cm. Find the area of the rectangle, if OC = 7 cm.

Q. 3. Two identical circles intersect at (0, 5) and (0, -5). Each circle passes through the centre of the other circle. Find the area of either circle.

Q.

Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two . Find the area enclosed between these circles.

1. $8c{m}^2$

2. $2.9c{m}^2$v

3. $2c{m}^2$

4. $4c{m}^2$

Q.

The perimeter of a certain sector of a circle is equal to the length of the arc of a semi-circle having the same radius ; express the angle of the sector in degrees, minutes and seconds.

Q.

The cross section of a canal is in a shape of a trapezium. If the canal is 12 m wide at the top and 8 m wide at the bottom and the area of its cross – section is 84 $m^2$, determine its depth.

1. 9.4 m

2. 6.8 m

3. 7.2 m

4. 8.4 m

Q.

A circle is cut into 16 equal sectors and the sectors are arranged as shown below.


The given figure can be visualised as

1. Rectangle

2. Square

3. Hexagon

4. None of these

Q.

What is the length of an arc which subtends angle $\theta$ (degrees) at the center in a circle of radius r?

1. $\frac{\pi r\theta }{180}$

2. $\frac{\pi r\theta }{360}$

3. $\frac{\pi r\theta }{60}$

4. $\frac{\pi r\theta }{90}$

Q.

1. x = (y × θ)/180

2. y = (x × θ)/360

3. y = (x × θ)/260

4. x = (y × θ)/360

Q. In fig. 9.34, seg AB and seg CD are perpendicular diameter of a circle with radius 7 cm. seg AO is the diameter of smaller circle. Find the area of shaded region.

Q. If the radius of a circle is 6 cm and $\theta$ is ${30}^{\circ }$, then find the length of the arc of the circle.

Q. If $x\ne 0$ and $x+\frac{1}{x}=2$, then:
$x^2+\frac{1}{x^2}=x^3+\frac{1}{x^3}=x^4+\frac{1}{x^4}$

1. True
2. False

Q.

AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O. If $\angle AOB={30}^{\circ }$, find the area of the shaded region.

1. $\frac{208}{5}c{m}^2$

2. $\frac{358}{6}c{m}^2$

3. $\frac{308}{3}c{m}^2$

4. $\frac{108}{3}c{m}^2$

Q.

In each of the figures below, find the area of the shaded part

Q.

In the figure given below, the radius of the circle is 42 cm. The angle in the sector is ${60}^{\circ }$​. What is the area of the segment APB?

1. $924sqcm$

2. $441\sqrt{3}sqcm$

3. $924-441\sqrt{3}sqcm$

4. $1743sqcm$

Q. Find the area of regular pentagon having length of the side as 5 cm and the radius of inscribed circle is 4.5 cm.

Q.

1. x = (y × θ)/180

2. x = (y × θ)/360

3. y = (x × θ)/360

4. y = (x × θ)/260

Q.

The given figure is a sector of a circle of radius 20 cm. Find the perimeter of the sector.
(Take $\pi$ = 3.14)

1. 55.25 cm

2. 60.93 cm

3. 65.48 cm

4. 70.17

Q. In the fig. 9.14 the radius of an inscribed circle in the square is 10 cm. Find the area of shaded portion.

Q.

The area of a sector (in $c{m}^2$ )of a circle with radius 6 cm if angle of the sector is ${70}^{\circ }$ will be __ $c{m}^2$. ( Take $\pi$ = $\frac{22}{7}$)

1. 22

2. 36

3. 44

4. 11

Q.

A pond is in shape of trapezium. A bridge is to be constructed such that the bridge is perpendicular to the parallel sides. It is given that the area of a pond is 1080 $m^2$ and the lengths of its parallel sides are 55.6 m and 34.4 m. Find the length of the bridge.

1. 56 m

2. Data insufficient

3. 24 m

4. 48 m

Q. The mean of the number $\frac{{}^{50}{\text{C}}_0}{1}$, $\frac{{}^{50}{\text{C}}_2}{3}$, $\frac{{}^{50}{\text{C}}_4}{5}$, ..., $\frac{{}^{50}{\text{C}}_{50}}{51}$ equals,

1. $\frac{2^{50}}{51}$
2. $\frac{2^{49}}{51}$
3. $\frac{2^{49}}{39\times 17}$
4. none of these