Area of Circle

Q. The perimeter of a square, whose each side is 22 cm, is same as the circumference of a circle. Find the area of the circle.

1. $516c{m}^2$​
2. $716c{m}^2$​
3. $154c{m}^2$​
4. $616c{m}^2$

Q.

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.

1. $100c{m}^2$

2. $346c{m}^2$

3. $178c{m}^2$

4. $378c{m}^2$

Q. The radius of the circle is 7cm and the angle subtended by the arc is 60°. If the area of $\Delta$OAB is $21c{m}^2$, then the area of segment ABP is

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

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. Two circles touch each other internally. The sum of their areas is 130π cm^2 and the distancebetween their centres is 8 cm. Find the radii of the two circles.

Q.

If the circumference of a circle is 528 cm, then its area is ______ $c{m}^2$.

$(\pi =\frac{22}{7})$

1. 22176

2. 22576

3. 23176

4. 24576

Q.

[Two friends discussing over a 2-dimensional figure]

Arjun: Area is the length of the rope required to surround the figure.

Shubh: The quantity of cloth required to cover the figure exactly, is called its area.

Pick the correct option.

1. Arjun and Shubh both mean the same thing

2. Arjun is right and Shubh is wrong

3. Arjun is wrong and Shubh is right

4. Both of them are wrong

Q.

Question 7
The inner diameter of a circular well is 3.5 m. It is 10m deep. Find
(i) Its inner curved surface area,
(ii) The cost of plastering this curved surface at the rate of $Rs.40per{m}^2.[Assume\pi =\frac{22}{7}]$

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. A gear system has the driving wheel of radius $2cm$ and driven wheel of radius $20cm$. What is the gear ratio ?

1. $1:2$
2. $11:10$
3. $1:10$
4. $1:1$

Q.

Consider the following circle and choose the incorrect option.

1. Region in green = Minor sector
2. Region in green + Region in blue = Minor sector
3. Region in red = Major sector
4. Region in blue = Minor segment

Q. 25. A glass cylender with diameter 20cm has water to a height of 9cm.A metal cube of 8cm edge is immersed in it completely . calculate the height by which water will rise in cylinder (take π=3.142)

Q. Which of the following statements is/are true?

1. Area of a circle can be derived by cutting the circle into a triangle.
2. Area of a circle can be derived by dividing the circle into segments and rearranging the segments to form a rectangle
3. Area of a circle can be derived by dividing the circle into segments and rearranging the segments to form a circle.
4. None of the above.

Q.

In the square carpet given below, find the area of the orange region.

Q. A well with 10m inside diameter is dug 3 14 m deep.Earth taken out of it is spread all around to form an embankment .Find the height of embankment

Q. The radius of the circle is 7 cm and the angle subtended by the arc is 60°. If the area of $\Delta$OAB is $21c{m}^2$, then find the area of segment ABP.

Q. The diameter of a circle is $28cm$. Find its circumference

1. $32cm$
2. $48cm$
3. $98cm$
4. $88cm$

Q. If one-quarter of a circle of radius of 14 cm is removed, then the remaining portion is known as the _____ segment and it's area is ____.

1. minor, $308c{m}^2$
2. minor, $462c{m}^2$
3. major, $308c{m}^2$
4. major, $462c{m}^2$

Q. The radius of a circle is $14m$, then the circumference of a circle is

1. $88m$
2. $616m$
3. $154m$
4. none of these

Q.

The area of a circular playground is $22176m^2$. Find the cost of fencing this ground at the rate of ₹ 50 per m.

1. $₹20000$

2. $₹26000$

3. $₹12400$

4. $₹26400$

Q.

what is the area of hemisphere

Q.

The diameter of the moon is one fourth of the diameter of the earth.

Find the ratio of their surface areas. Also find the percentage increase intheir surface areas.

Q. If two circles are equal, then their ........ are equal.

1. chords
2. radii
3. tangents
4. central angles

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.

Q.

1. $44c{m}^2$
2. $40c{m}^2$
3. $42c{m}^2$
4. $45c{m}^2$

Q. Find circumference of a circle of diameter $4.2cm$.

1. $13.2cm$
2. $13.7cm$
3. $14.9cm$
4. $14.2cm$

Q.

If the sum of the circumferences of two circles with radii ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ is equal to the circumference of a circle of radius $R$, then

1. $R_1+R_2=R$

2. $R_1+R_2>R$

3. $R_1+R_2<R$

4. Nothing definite can be said about the relation among $R_1,R_{2}andR.$

Q. A cylinder with radius $r$ and height $h$ is closed on the top and bottom. Which of the following expressions represents the total surface area of this cylinder?

Q. The area bounded by the loop of the curve $4y^2=x^2(4-x^2)$ is

1. $\frac{7}{3}$ sq. units
2. $\frac{8}{3}$ sq. units
3. $\frac{11}{3}$ sq. units
4. $\frac{16}{3}$ sq. units

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(${53}^{\circ }$) = $\frac{3}{5}$.