RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 18. Area of Circle, Sector and Segment

Subject: Maths - Class 10th

Q. No. 51 of Exercise 18A

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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.

Given:

Radius of Circle = 35 cm


∠AOB = 90°


∵ Area of Sector = × πr2


= × × 35 × 35


= cm2


∵ ∆ AOB is right-angled triangle.


∴ Area of ∆ AOB = × OA × OB


= × 35 × 35


= cm2


Now, Area of Minor Segment ACB


= Area of Sector – Area of ∆AOB


= - = = 350 cm2


Area of Circle = πr2


= × 35 × 35


= 22 × 5 × 35


= 3850 cm2


Thus, Area of Major Segment = Area of Circle – Area of Minor Segment = 3850 – 350 = 3500 cm2


Hence, the area of the major segment is 3500 cm2.


Chapter Exercises

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

More Exercise Questions

1

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2

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

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4

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5

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6

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7

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8

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9

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

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11

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12

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13

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14

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15

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16

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17

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18

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19

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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

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24

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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

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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

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

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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

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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