RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 18. Area of Circle, Sector and Segment

Subject: Maths - Class 10th

Q. No. 15 of Formative Assessment (Unit Test)

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15

In the given figure, an equilateral triangle has been inscribed in a circle of radius 4 cm. Find the area of the shaded region. [Take π = 3.14 and √3 = 1.73]


Radius of circle = R = 4 cm


OD perpendicular to AB is drawn


ΔABC is equilateral triangle,


∠A = ∠B = ∠C = 60°


∠OAD = 30°


OD/AO = sin 30°


AO = 4 cm



OD = 1/2 × 4 cm


OD = 2 cm


AD2 = OA2 – OD2


= 42 – 22 = 16 – 4 = 12 cm2


AD = 2√3 cm


AB = 2 × AD


= 2 × 2√3 cm = 4√3 cm


Area of triangle ABC = √3/4 × AB2


= √3/4 × 4√3 × 4√3


= 20.71 cm2


Area of circle = πR2


= 3.14 × 4 × 4 cm2


= 50.24 cm2


Area of shaded region = 29.53 cm2


Chapter Exercises

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

More Exercise Questions

1

In the given figure, a square OABC has been inscribed in the quadrant OPBQ. If OA = 20 cm then the area of the shaded region is [take π = 3.14]
2

The diameter of a wheel is 84 cm. How many revolutions will it make to cover 792 m?
3

The area of a sector of a circle with radius r, making an angle of x° at the centre is x
4

In the given figure, ABCD is a rectangle inscribed in a circle having length 8 cm and breadth 6 cm. If π = 3.14 then the area of the shaded region is
5

The circumference of a circle is 22 cm. Find its area. [Take π = 22/7]
6

In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find the length of the arc.
7

The minute hand of a clock is 12 cm long. Find the area swept by it in 35 minutes.
8

The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm. Find the area of the sector.
9

A chord of a circle of radius 14 cm makes a right angle at the centre. Find the area of the sector.
10

In the give figure, the sectors of two concentric circles of radii 7 cm and 3.5 cm are shown. Find the area of the shaded region.
11

A wire when bent in the form of an equilateral triangle encloses an area of 121√3 cm2. If the same wire is bent into the form of a circle, what will be the area of the circle? [Take π = 22/7]
12

The wheel of a cart is making 5 revolutions per second. If the diameter of the wheel is 84 cm, find its speed in km per hour. [Take π = 22/7]
13

OACB is a quadrant of a circle with centre O and its radius is 3.5 cm. If OD = 2 cm, find the area of (i) the quadrant OACB

(ii) the shaded region. [Take π = 22/7]
14

In the given figure, ABCD is a square each of whose sides measures 28 cm. Find the area of the shaded region. [Take π = 22/7]
15

In the given figure, an equilateral triangle has been inscribed in a circle of radius 4 cm. Find the area of the shaded region. [Take π = 3.14 and √3 = 1.73]
16

The minute hand of a clock is 7.5 cm long. Find the area of the face of the clock described by the minute hand in 56 minutes.
17

A racetrack is in the form of a ring whose inner circumference is 352 m and outer circumference is 396 m. Find the width and the area of the track.
18

A chord of a circle of radius 30 cm makes an angle of 60° at the centre of the circle. Find the areas of the minor and major segments. [Take π = 22/7 and √3 = 1.732.]
19

Four cows are tethered at the four corners of a square field of side 50 m such that each can graze the maximum unshared area. What area will be left ungrazed? [Take π = 3.14]
20

A square tank has an area of 1600 m2. There are four semicircular plots around it. Find the cost of turfing the plots at Rs. 12.50 per m2. [Take π = 3.14]

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