RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 18. Area of Circle, Sector and Segment

Subject: Maths - Class 10th

Q. No. 25 of Exercise 18A

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25

Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimensions 14 cm × 7 cm. Find the area of the remaining cardboard.

Given:

Length of the rectangular cardboard = 14 cm


Breadth of the rectangular cardboard = 7 cm


Ques25.bmp


∵ Area of rectangle = length × breadth


∴ Area of cardboard = 14 × 7 = 98 cm2


Let the two circles with equal radii and maximum area have a radius of ‘r’ cm each.


Then, 2r = 7


r = cm


∵ Area of circle = πr2


∴ Area of two circular cut outs = 2 × πr2


= 2 × × ×


= 11 × 7 = 77 cm2


Thus, the area of remaining cardboard = 98 – 77 = 21 cm2


Hence, the area of remaining cardboard is 21 cm2.


Chapter Exercises

Exercise 18A
Exercise 18B
Multiple Choice Questions (MCQ)
Formative Assessment (Unit Test)

More Exercise Questions

1

The difference between the circumference and radius of a circle is 37 cm. Using π = 22/7, find the circumference of the circle.
2

The circumference of a circle is 22 cm. Find the area of its quadrant.
3

What is the diameter of a circle whose area is equal to the sum of the areas of two circles of diameter 10 cm and 24 cm?
4

If the area of a circle is numerically equal to twice its circumference, then what is the diameter of the circle?
5

What is the perimeter of a square which circumscribes a circle of radius a cm?
6

Find the length of the arc of a circle of diameter 42 cm which subtends an angle of 60° at the centre.
7

Find the diameter of the circle whose area is equal to the sum of the areas of two circles having radii 4 cm and 3 cm.
8

Find the area of a circle whose circumference is 8π.
9

Find the perimeter of a semicircular protractor whose diameter is 14 cm.
10

Find the radius of a circle whose perimeter and area are numerically equal.
11

The radii of two circles are 19 cm and 9 cm. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.
12

The radii of two circles are 8 cm and 6 cm. Find the radius of the circle having area equal to the sum of the areas of the two circles.
13

Find the area of the sector of a circle having radius 6 cm and of angle 30°.
14

In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find the length of the arc.
15

The circumferences of two circles are in the ratio 2:3. What is the ratio between their areas?
16

The areas of two circles are in the ratio 4:9. What is the ratio between their circumferences?
17

A square is inscribed in a circle. Find the ratio of the areas of the circle and the square.
18

The circumference of a circle is 8 cm. Find the area of the sector whose central angle is 72°.
19

A pendulum swings through an angle of 30° and describes an arc 8.8 cm in length. Find the length of the pendulum.
20

The minute hand of a clock is 15 cm long. Calculate the area swept by it in 20 minutes.
21

A sector of 56°, cut out from a circle, contains 17.6 cm2. Find the radius of the circle.
22

The area of the sector of a circle of radius 10.5 cm is 69.3 cm2. Find the central angle of the sector.
23

The perimeter of a certain sector of a circle of radius 6.5 cm is 31 cm. Find the area of sector.
24

The radius of a circle is 17.5 cm. Find the area of the sector enclosed by two radii and an arc 44 cm in length.
25

Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimensions 14 cm × 7 cm. Find the area of the remaining cardboard.
26

In the given figure, ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is also drawn. Find the area of the shaded region.
27

From a rectangular sheet of paper ABCD wit AB = cm and AD = 28 cm, a semicircular portion wit BC as diameter is cut off. Find the area of the remaining paper.
28

In the given figure, OABC is a square of side 7 cm. If COPB is a quadrant of a circle wit centre C find the area of the shaded region.
29

In the given figure, three sectors of a circle of radius 7 cm, making angles of 60°, 80° and 40° at the centre are shaded. Find the area of the shaded region.
30

In the given figure, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and 3.5 cm with centre O. If ∠POQ = 30°, find the area of the shaded region.
31

In the given figure, find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC are semicircle.
32

In the given figure, the shape of the top of a table is that of a sector of circle with centre O and ∠AOB = 90°. If AO = OB = 42 cm, then find the perimeter of the top of the table.
33

In the given figure, ABCD is a square of side 7 cm, DPBA and DQBC are quadrants of circles each of the radius 7 cm. Find the area of shaded region.
34

In the given figure, OABC is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region.
35

Find the perimeter of shaded region in the figure, if ABCD is a square of side 14 cm and APB and CPD are semicircles.
36

In a circle of radius 7 cm, a square ABCD is inscribed. Find the area of the circle which is outside the square.
37

In the given figure, APB and CQD are semicircle of diameter 7 cm each, while ARC and BSD are semicircles of diameter 14 cm each. Find the (i) perimeter, (ii) area of the shaded region.
38

In the given figure, PSR, RTQ and PAQ are three semicircles of diameter 10 cm, 3 cm and 7 cm respectively. Find the perimeter of shaded region.
39

In the given figure, a square OABC is inscribed in a quadrant OPBQ of a circle. IF OA = 20 cm, find the area of the shaded region. [Use π = 3.14]
40

In the given figure, APB and AQO are semicircles and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region.
41

Find the area of a quadrant of a circle whose circumference is 44 cm.
42

In the given figure, find the area of the shaded region, where ABCD is a square of side 14 cm and all circles are of the same diameter.
43

Find the area of the shaded region in the given figure, if ABCD is a rectangle wit sides 8 cm and 6 cm ad O is the centre of the circle.
44

A wire is bent to form a square enclosing an area of 484 m2. Using the same wire, a circle is formed. Find the area of the circle.
45

A square ABCD is inscribed in a circle of radius ‘r’. Find the area of the square.
46

The cost of fencing a circular field at the rate of Rs. 25 per meter is Rs. 5500. The field is to be ploughed at the rate of 50 paise per m2. Find the cost of ploughing the field. [Take π = 22/7]
47

A park is in the form of a rectangle 120 m by 90 m. At the centre of the park, there is a circular lawn as shown in the figure. The area of the park excluding the lawn is 2950 m2. Find the radius of the circular lawn. [Given, π = 3.14]
48

In the given figure PQSR represents a flower be. If OP = 21 m and OR = 14 m, find the area of the flower bed.
49

In the given figure, O is the centre of the bigger circle, and AC is its diameter. Another circle with AB as diameter is drawn. If AC = 54 cm and BC = 10 cm, find the area of the shaded region.
50

From a thin metallic piece in the shape of a trapezium ABCD in which AB ∥ CD and ∠BCD = 90°, a quarter circle BFEC is removed. Given, AB = BC = 3.5 cm and DE = 2 cm, calculate the area of remaining (shaded) part of metal sheet.
51

Find the area of the major segment APB of a circle of radius 35 cm and ∠AOB = 90°, as shown in the given figure.

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