11. Areas Related to Circles

SEBA Class 10 Maths Chapter 11. Areas Related to Circles

Chapter 11. Areas Related to Circles

Class 10 Maths Chapter 11. Areas Related to Circles Multiple Choice Qustions and Solutions

Question : Area of a sector of angle P (in degree) of a circle with radius R is : [SEBA 2015]

(a) (b)

Solution: (d)

Question : If the circumference of a circle is 44 cm , then its area is : [SEBA 2016]

(a) 276 (a) 44

Solution: (d) 154 .

[ A/Q,

The area of the circle ]

Question : The area of the circle that can be inscribe in a square of side 6 cm is : [ SEBA 2017]

(a) (b)

Solution: (d) .

[ The square of the side cm and the radius cm

The area of the circle

]

Question : If the circumference of a circle is 22 cm , then the area of a quadrant of the circle is : [SEBA 2018]

(a) (b) 77

Solution : (a)

[ A/Q ,

The area of a quadrant of the circle ]

Question : The degree measure of the angle at the centre of a circle is 1 . The area of the sector is : [SEBA 2019]

(a) (b)

Solution: (d)

[ We have,

; ]

Question : The degree measure of the angle at the centre of a circle is . The length of a arc of the sector is :

(a) (b) (c) (d) Where is the radius of the circle . [ SEBA 2020]

Solution: (b)

[We have,

; ; ]

Question : If the sum of the areas of two circles with radii and is equal to the area of a circle of radius,then

(a) (b)

Solution: (b)

Question : If the perimeter of a circle is equal to that of a square , then the ratio of their areas is :

(a) 22 : 7 (b) 14 : 11 (c) 7 : 22 (d) 11 : 14

Solution : (b) 14 : 11 .

[ let be the radius of the circle and be side of the square .

A/Q ,

]

Question : If the sum of the circumference of two circles with radii and is equal to the circumference of a circle of radius , then

(a) (b)

Solution: (a)

Question : If the radius of a circle is doubled , then the ratio of the areas of the new circle to the area of the given circle is :

(a) 2 : 1 (b) 1 : 2

Solution: (d) 4 : 1

[ Here , and

]

Question : If the area of a circle is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm, then diameter of the larger circle (in cm) is : [CBSE 2012]

(a) 34 (b) 26 (c) 17 (d) 14

Solution: (b) 26

[ Here , cm and cm

A/Q ,

Therefore, the diameter cm cm ]

Question : If is taken as , the distance (in metres) covered by a wheel of diameter 35 cm , in one revolution is : [CBSE 2013]

(a) 2.2 (b) 1.54 (c) 9.625 (d) 96.25

Solution: (b) 1.54

[ Here , Diameter cm and Radius cm

Therefore, the distance covered by a wheel in one revolution

m m m ]

Class 10 Areas Related to Circles Fill in the blank :

Question : The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is ............. .

Solution: 50 cm .

[ Here , cm and cm

A/Q ,

Therefore , the diameter cm cm ]

Question : Area of a sector to circle of radius 36 cm is , then the length arc of the corresponding arc of the circle is ..............

Solution: .

[ Here , cm

A/Q,

Therefore, the length arc of the corresponding arc of the circle

]

Class 10 Areas Related to Circles Answers following the questions :

Question : Find the length of the arc of a circle of diameter 42 cm which subtends angle of 60° at the circle ? [CBSE 2012]

Solution: Here , radius and

Therefore, the length of the arc of a circle

Question : Find the area of a quadrant of a circle whose circumference is . [ CBSE 2014]

Solution: We have,

Therefore , the area of quadrant of the circle

Question : The difference between the circumference and radius of a circle is 37 cm . Find the area of the circle . [ CBSE 2013]

Solution: let r be the radius of the circle .

Therefore, the area of circle .

Question : Find the area of a sector of a circle of radius 28 cm and central angle 45° .

Solution: Here , cm and

Therefore, the area of a sector of a circle

Question : The radii of radius circles are 19 cm and 9 cm respectively . Find the radius of the circle which has circumference equal to the sum of the circumference of the two circles.

Solution: let be the radius of the new circle .

Here , cm and cm

A/Q ,

Class 10 Areas Related to Circles 2 Marks Questions and Solutions

SECTION = B

Question : Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60° .

Solution: Here , cm and

Therefore, the area of a sector of a circle

Question : The cost of fencing a circular field at the rate of Rs. 24 per metre is Rs. 5280 , then find the radius of field .

Solution: let be the radius of the circular field .

The length of the fence field m

A/Q ,

Question : An umbrella has 8 ribs which are equally spaced and the umbrella to be a flat circle of radius 45 cm , find the area between the two consecutive ribs of the umbrella .

Solution: Here , cm

The area between the two consecutive ribs of the umbrella

Question : If the area of a sector of a circle of radius 14 cm is . Find the length of the corresponding arc of the sector . [CBSE 2011]

Solution: Here , cm

A/Q ,

Therefore, the length of the corresponding arc of the sector

cm cm

Class 10 Areas Related to Circles 3 Marks Questions and Answers

Question : 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 .

Solution : Here , cm

The area between the two consecutive ribs of the umbrella

Question : 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 :

(i) the total length of the silver wire required .

(ii) the area of each sector of the brooch .

Solution: (i) Here, diameter and Radius

The circumference

The length of the wire required to make 5 diameters

Therefore, the total length of the silver wire required

(ii) The angle of each brooch

So, the area of each sector of the brooch

Question : 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 ]

Solution: Here , cm and

(i) The area of the corresponding minor segment Area of sector – area of triangle

(ii) Here, ,

Area of major sector of a circle

Question : 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 and )

Solution : Here, and

The area of the corresponding segment of the circle

Question : A chord of a circle of radius 15 cm subtends an angles of 60° at the centre . Find the areas of the corresponding minor and major segments of the circle . [SEBA 2017]

Solution: Here , radius cm ,

Area of the minor segment

= Area of the sector – Area of the triangle formed by radius and chord

Area of major segment Area of the circle – Area of the minor segment

Question : 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 .

Solution: Here, Radius cm and

(i) the length of an arc of a sector of a circle

(ii) the area of the sector formed by the arc

(iii) Here, OA = OB = 21 cm and

So, OAB be an equilateral triangle .

Area of triangle OAB

The area of segment formed by chord = Area of sector – Area of triangle

Question : 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 (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 ) [SEBA 2023]

Solution : Since , ABCD is a square .

So, AB = BC = CD = AD = 15 cm

(i) Here, ,

Therefore, the area of the field in which the horse can graze

(ii) Here, , and

The increasing area of the field

Question : Find the area of the segment AYB shown in given figure, if radius of the circle is 21 cm and . (Use π = 22/7 )

Solution : Here,

[ Note : We know that , area of the minor segment of the circle Area of triangle

]

The area of the segment AYB