RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 18. Area of Circle, Sector and Segment

Subject: Maths - Class 10th

Q. No. 23 of Exercise 18A

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23

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

Given:

Radius of circle = 6.5 cm


Perimeter of sector = 31 cm


Now, Perimeter of sector = 2 × radius + Length of arc


∵ Length of arc = × 2r × 2πr


∴ Perimeter of sector = 2 × r + × 2r × π


= 2r × [1 + × π]


31 = 2 × 6.5 × [1 + × ]


31 = 13 × [1 + × ]


= 1 + ×


- 1 = ×


= ×


θ = × 360 × …………………. (i)


∵ Area of sector = × πr2


∴ using (i), we have


Area = × 360 × × × × 6.5 × 6.5


= 18 × 3.25 = 58.5 cm2


Hence, the area of the sector is 58.5 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

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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

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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

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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

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18

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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

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21

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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

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26

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27

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28

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29

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30

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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

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34

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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

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38

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39

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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

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44

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45

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

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47

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48

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49

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50

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51

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