Area of Circle

Q. $Assertion:$ In a circle of radius $6cm$, the angle of a sector is $60°$. Then the area of the sector is $18\frac{6}{7}c{m}^2.$
$Reason:$ Area of the circle with radius $r$ is $\pi r^2$.

Q. Three circles each of radius 7 cm are placed in such a way that each of them touches the other two externally. The empty area enclosed between the circles is:$(\text{Take}\pi =\frac{22}{7})$

[1 mark]

1. $88.7c{m}^2$
2. $8.87c{m}^2$
3. $78.7c{m}^2$
4. $7.87c{m}^2$

Q. 23. An equilateral triangle has area A root 3.Three circles are drawn with their centres at the vertices of the triangle.Diameter of each circle is equal to the length of each side of the triangle.The area of the triangle not included in any of the circles is?

Q.

In a circle of radius 20 cm, a chord subtends a right angle at the centre. Find the area of the major segment: (use $\pi$ = $\frac{22}{7}$)

1. 2635.6 ${cm}^2$
2. 1391.9 ${cm}^2$
3. 1125.2 ${cm}^2$
4. 1142.85 ${cm}^2$

Q.

The circumference of a circle is 39.6 cm. Find its area.

Q. 5. The circumference of a given circular Park is 55 m. It is surrounded by a path of uniform width 3.5m. Find the area of the path

Q. Question 7
The area of the circle that can be inscribed in a square of side 6 cm is
(A) $36\pi c{m}^2$
(B) $18\pi c{m}^2$
(C) $12\pi c{m}^2$
(D) $9\pi c{m}^2$

Q. Question 4
The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?

Q. Question 5 (iii)
In a circle of radius 21 cm, an arc subtends an angle of ${60}^{\circ }$ at the centre. Find:
(iii) area of the segment formed by the corresponding chord

Q. 18. A well of diameter 3m , is dug 14m deep. The earth taken out of it has been spread evenly all around it to a width of 4m , to form a embankment . Find the height of embankment ?

Q. If $r_1=9cm$ and $r_2=5cm$, then find the area of the shaded region. (Use $\pi =\frac{22}{7}$)

1. 176

Q. Question 7
The area of the circle that can be inscribed in a square of side 6 cm is
(A) $36\pi c{m}^2$
(B) $18\pi c{m}^2$
(C) $12\pi c{m}^2$
(D) $9\pi c{m}^2$

Q. Question 2
The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.

Q. 34. An equilateral triangle has area A\sqrt{}3. Three circles are drawn with their centres at the vertices of the triangle . Diameter of each circle is equal to the length of each side of the triangle. The area of the triangle not include in any of the three circles is

Q.

Question 11
On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.

Q. The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

Q. Question 1
If the sum of the areas of two circles with radii $R_1$ and $R_2$ is equal to the areas of a circle of radius R, then:
(A) $R_1+R_2=R$
(B) $R_1^2+R_2^2=R^2$
(C) $R_1+R_2<R$
(D) $R_1^2+R_2^2<R_2$

Q. What is the area of the largest triangle that can be inscribed in a semi-circle of radius 'r'?

1. r*r
2. 2r*r
3. 1/3(r*r)
4. 1/2(r*r)

Q. A square PQRS of side 22 cm is divided into five equal parts. The central part is circular and the lines, PA, QB, RC and SD lie along the digonals PR and QS of the square.

Find
(i) The circumference of the central part.
(ii) The perimeter of the part PADS.

Q. Find the area of the shaded region in figure. Where ABCD is a square of side $10cm$. (Use $\pi =3.14$)

1. $32c{m}^2$
2. $41c{m}^2$
3. $49c{m}^2$
4. $57c{m}^2$

Q. 38. A well of inner diameter 14m is dug out to a depth of 12m.Earth taken out of it has been evenly spread all around it to a width of 7m to form an embankment.Find the height of embankment so formed.

Q. A horse is tied outside a room with a rope of length 10 m. It can graze on the rest of the field. How much area can it graze?

1. $\text{90}\pi m^2$
2. $\text{75}\pi m^2$
3. $\text{81.25}\pi m^2$
4. $\text{86.25}\pi m^2$

Q. 75. A well is dug 3m and 14m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4m to form an embankment. Find the height of the embankment.

Q. Three semicircles each of diameter $3cm$, a circle of diameter $4.5cm$ and a semicircle of radius $4.5cm$ are drawn in the given figure. Find the area of the shaded region.

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 find the area of segment APBA.
$(\pi =\frac{22}{7})$

1. $5.8{cm}^2$

2. $4.7{cm}^2$

3. $8{cm}^2$

4. $1{cm}^2$

Q.

The area of a circle is 394.24 $c{m}^2$. Then the radius of the circle in cm is _______.

1. 11.4

2. 11.3

3. 11.2

4. 11.1

Q. Question 10
The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm abd 7 cm is
(A) 31 cm
(B) 25 cm
(C) 62 cm
(D) 50 cm

Q. For a wheel with circumference 44cm, match the following parameters.

1. 154
2. 14 cm
3. 7 cm
4. 44 cm

Q. Find the area of the given diagram

Q. The capacity of your cousin is one roti when the radius is 4 cm. The__ of the rotis made by your mother must be ${\frac{1}{4}}^{th}$ so that your cousin can eat 4 rotis.