Exercise 11.1 (NCERT) - Areas Related To Circles, Class 10
| Chapter 11 | Exercise 11.1 | Class 10 |
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Below are the Quick links for all questions of Exercise 11.1, Areas Related To Circles, Class 10.
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Below are the solutions of every question of exercise 11.1 of chapter 11, Circles, NCERT of class 10. YouTube video tutorial of every question is also embedded along with the written solution.
Question 1
Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.
Question 2
Find the area of a quadrant of a circle whose circumference is 22 cm.
Given
Circumference of circle, C = 22cm
We know that
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.
Given
Length of minute hand (radius) = r = 14cm
Angle swept in 5 minutes
Question 4
A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding :
(i) minor segment (ii) major sector. (Use 𝝅 = 3.14)
Triangle AOB is a right angled triangle
=> Base = 10cm, Height = 10cm
Area = 1/2 (Base * Height)
Question 5
In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find:
(i) the length of the arc (ii) area of the sector formed by the arc
(iii) area of the segment formed by the corresponding chord
You can finish the question here but in case you are asked to use the value of √3 = 1.732 then solve it further.
Question 6
A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle.
(Use pi = 3.14 and √3 = 1.73)
Given
Question 7
A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle.
(Use pi = 3.14 and √3 = 1.73)
Given
To find the area of triangle AOB, split the triangle into 2 equal right angled triangles by drawing a perpendicular OD on AB.
∠AOD = ∠BOD = 60°
See the video.
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 Fig. 11.8). Find
(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 pi = 3.14)
Given
Horse is tied at one corner, so grazing area is a quarter circle.
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 Fig. 11.9. Find :
(i) the total length of the silver wire required.
(ii) the area of each sector of the brooch.
Given
5 diameters divide the circle into 10 equal sectors.
(i) Total Length of Silver Wire
(ii) Area of Each Sector
Question 10
An umbrella has 8 ribs which are equally spaced (see Fig. 11.10). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.
Given
Umbrella has 8 equally spaced ribs. This means the circle is divided into 8 equal sectors.
Since there are equally spaced 8 sectors, hence angle formed by every sector is
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.
Given
Area swept by one wiper = Area of sector formed at angle 115 degrees
Question 12
To warn ships for underwater rocks, a lighthouse spreads a red coloured 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 pi = 3.14)
Given
Area of sea over which ships are warned
Question 13
A round table cover has six equal designs as shown in Fig. 11.11. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs. 0.35 per cm2.
(√3 = 1.7)
Given
Step 2: Area of triangle formed by 2 radii and the chord
This triangle is an equilateral triangle.
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
Given
p = Angle of the sector in degrees
R = Radius of the circle
Answer: D