Angle of a Sector

Q.

Four equal circles, each of radius a, touch each other. Show that the area between them is $\frac{6}{7}{a}^2$ (Take $\pi =\frac{22}{7}$)

Q.

The diameter of a coin is 1 cm(Fig). If four such coins be placed on a table so that the rim of each touches that of the other two, find the area of the shaded region. (Take $\pi =3.1416$)

Q. Question 7
In Fig. 12.25, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region.

Q.

Area of a sector of angle $p$ (in degrees) of a circle with radius $R$ is

1. $\frac{p}{180°}\times 2\mathrm{\pi R}$

2. $\frac{p}{180°}\times {\mathrm{\pi R}}^2$

3. $\frac{p}{360°}\times 2\mathrm{\pi R}$

4. $\frac{p}{720°}\times 2{\mathrm{\pi R}}^2$

Q. In a circle, area of minor sector is area of major segment.

1. equal to
2. greater than
3. less than

Q. If the area of a circle is $1386{\text{cm}}^2$, then its perimeter is

1. $176\text{cm}$
2. $132\text{cm}$
3. $148\text{cm}$
4. $144\text{cm}$

Q. A circular garden of radius 10m has a straight line fence between the two points on the boundary of the garden. The fence lies inside the garden arena. This fence separates the walking area which is a small region from the plants. The fence is at a distance of 6 m from the centre of the garden. Find the angle subtended by the fence with the center of the garden. It is given that cos(${53}^{\circ }$) = $\frac{3}{5}$.

1. ${53}^{\circ }$
2. ${37}^{\circ }$
3. ${212}^{\circ }$
4. ${106}^{\circ }$

Q. What will be the slope if a line is perpendicular to y-axis?

1. 0
2. 1
3. Not defined
4. -1

Q.

In a circle, a $60°$ sector has an area of $25\mathrm{\pi }$ $\text{square feet}$. What is the circumference? Leave your answer in terms of $\mathrm{\pi }$ and in simplest radical form.

Q.

A circular garden of radius 10m has a straight line fence between the two points on the boundary of the garden. The fence lies inside the garden arena. This fence separates the walking area which is a small region from the plants. The fence is at a distance of 6 m from the centre of the garden. Find the angle subtended by the fence with the center of the garden. It is given that cos(${53}^{\circ }$) = $\frac{3}{5}$.

1. ${37}^{\circ }$

2. ${106}^{\circ }$

3. ${212}^{\circ }$

4. ${53}^{\circ }$

Q. If $\alpha$ is the angle (in degrees) of a minor sector of a circle of radius $r$, then the area of the major sector is

1. $\frac{\pi r^2({360}^{\circ }-\alpha )}{{360}^{\circ }}$
2. $\frac{\pi r^2\alpha }{{360}^{\circ }}$
3. $\frac{2\pi r({360}^{\circ }-\alpha )}{{360}^{\circ }}$
4. $\frac{2\pi r\alpha }{{360}^{\circ }}$

Q. Distance travelled by a circular wheel of diameter $d$ cm in one revolution is $2\pi d$.

1. False
2. True

Q.

How do you find the radius of each circle if the area of the sector is $28$ and the angle is $150$ degrees?

Q.

Find the area of the sector of a circle of radius $14units$ subtended by an angle of $\frac{23\pi }{12}\mathrm{radians}$. Round your answer to the nearest tenth, and do not include the units in your answer.

Q.

There is a circular track with the distance of track from centre as 10 m. Ram runs a distance of 21 m on the track. What is the angle in degrees covered by Ram with respect to the centre of track?

1. ${76}^{\circ }$

2. ${63}^{\circ }$

3. ${56}^{\circ }$

4. ${90}^{\circ }$

Q. Question 8
If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r , then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle is this statement false? Why?

Q.

State true or false.
If the radius of a circle is $\frac{7}{\sqrt{\pi }}$ cm, then the area of the circle in $c{m}^2$ is $\frac{49}{{\pi }^2}$.

1. True

2. False

Q. The length of a chain used as the boundary of a semicircular park is $108$ cm. Find the area of the park.

Q. The diameter of a coin is $1$ cm . If four such coins be placed on a table so that the rim of each touches that of the other two, find the area of the shaded region. (Take $\pi =3.1416$)

Q.

A circular garden of radius 10 m is divided into two parts by a straight line fence. Smaller part is the walking area and flowers are planted in the larger part. The fence is at a distance of 6 m from the centre of the garden. What is the walking area in $m^2$? It is given that cos 53°= $\frac{3}{5}.$

1. $36m^2$

2. $44.5m^2$

3. $12m^2$

4. $72m^2$

Q. A man looks from the top of a vertical tower 30 metres high at a marked point upon the horizontal plane on which the tower stands. The angle of depression of this point is ${30}^0.$ The distance of the marked point from the foot of the tower is

1. $\frac{30}{\sqrt{3}}$m
2. 30 m
3. $30\sqrt{3}$m
4. $\frac{30\sqrt{3}}{2}$m

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.

___

Q. The slope of a straight line parallel to x - axis is:

1. 0.5
2. 1
3. 0
4. Not defined

Q. If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius $2r,$ then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of other circle. Is this statement false ? Why ?

1. True
2. False

Q. Area of a circle with diameter, $D$ is $\frac{\pi D^2}{4}$.

1. False
2. True

Q.

What would be the area of right isosceles triangle of side length a?

1. $\frac{a^2}{4}$

2. $2a^2$

3. $a^2$

4. $\frac{a^2}{2}$