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NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles Ex 12.2

NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles Ex 12.2 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles Ex 12.2.

  • Areas Related to Circles Class 10 Ex 12.1
  • Areas Related to Circles Class 10 Ex 12.2
  • Areas Related to Circles Class 10 Ex 12.3
Board CBSE
Textbook NCERT
Class Class 10
Subject Maths
Chapter Chapter 12
Chapter Name Areas Related to Circles
Exercise Ex 12.2
Number of Questions Solved 14
Category NCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles Ex 12.2

Ex 12.2 Class 10 Maths Question 1.
Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.
Solution:
Given: Radius of a sector, r = 6 cm and angle of a sector, θ = 60°
NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles 6

Did you check Areas related to circles formulas ?

Ex 12.2 Class 10 Maths Question 2.
Find the area of a quadrant of a circle whose circumference is 22 cm.
Solution:
Circumference of a circle = 22 cm [Given]
NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles 7

Ex 12.2 Class 10 Maths Question 3.
The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
Solution:
Angle described by the minute hand in 60 minutes = 360°
Angle described by the minute hand in 5 minutes
NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles 8

Ex 12.2 Class 10 Maths Question 4.
A chord of a circle of radius 10 cm subtends a right angle at the center. Find the area of the corresponding:
(i) minor segment
(ii) major segment (Use π = 3.14)
Solution:
NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles 9

Ex 12.2 Class 10 Maths Question 5.
In a circle of radius 21 cm, an arc subtends an angle of 60° at the center. Find:
(i) length of the arc.
(ii) area of the sector formed by the arc.
(iii) area of the segment formed by the corresponding chord.
Solution:
NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles 10
NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles 11

Ex 12.2 Class 10 Maths Question 6.
A chord of a circle of radius 15 cm subtends an angle of 60° at the center. Find the areas of the corresponding minor and major segments of the circle. (Use π = 3.14 and √3 = 1.73)
Solution:
NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles 12
NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles 13

Ex 12.2 Class 10 Maths Question 7.
A chord of a circle of the radius 12 cm subtends an angle of 120° at the center. Find the area of the corresponding segment of the circle. (Use π = 3.14 and √3 = 1.73).
Solution:
NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles 14
NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles 15

Ex 12.2 Class 10 Maths Question 8.
A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see figure). Find:
NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles 16
(i)
the area of that part of the field in which the horse can graze.
(ii) the increase in the grazing area if the rope were 10 m long instead of 5 m. (Use π = 3.14)
Solution:
NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles 17

Ex 12.2 Class 10 Maths Question 9.
A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in figure.
Find:
byjus class 10 maths Chapter 12 Areas Related to Circles 18

(i) the total length of the silver wire required.
(ii) the area of each sector of the brooch.
Solution:
byjus class 10 maths Chapter 12 Areas Related to Circles 19
byjus class 10 maths Chapter 12 Areas Related to Circles 20

Ex 12.2 Class 10 Maths Question 10.
An umbrella has 8 ribs which are equally spaced (see figure). Assuming umbrella to be a flat circle of radius / 45 cm, find the area between the two consecutive ribs of the umbrella.
byjus class 10 maths Chapter 12 Areas Related to Circles 21
Solution:
byjus class 10 maths Chapter 12 Areas Related to Circles 22

Ex 12.2 Class 10 Maths Question 11.
A car has two wipers which do not overlap.
Each wiper has a blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades.
Solution:
The blade of each wiper sweeps in the form of a sector of radius 25 cm.
The sector angle, θ = 115°  [Given]
∴ The area covered  by one blade
\(=\frac { { 115 }^{ \o } }{ { 360 }^{ \o } } \times \pi \times \left( 25 \right) ^{ 2 }\)
byjus class 10 maths Chapter 12 Areas Related to Circles 23

Ex 12.2 Class 10 Maths Question 12.
To warn ships for underwater rocks, a lighthouse spreads a red colored light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (Use π = 3.14)
Solution:
NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles 24

Ex 12.2 Class 10 Maths Question 13.
A round table cover has six equal designs as shown in the figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹0.35 per cm². (Use √3= 1.7)
NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles 25
|Solution:
NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles 26
NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles 27

Ex 12.2 Class 10 Maths Question 14.
Tick the correct answer in the following: Area of a sector of angle p (in degrees) of a circle with radius R is
NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles 28
Solution:
Area of a sector with radius R and angle P
NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles 29
Hence, the correct answer is (d).

We hope the NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles Ex 12.2 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles Ex 12.2, drop a comment below and we will get back to you at the earliest.

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