12. Areas Related to Circles

Circles

Chapter 12. Areas Related to Circles

Class 10 Maths Chapter 12 Areas Related to Circles : Multiple Choice Questions , Answer following the Questions , Fill in the blanks , 2 Marks Questions , 3 Marks Question and Solutions :

Class 10 Areas Related to Circles Multiple Choice Qustions and Solutions

SECTION = A

Q1. Area of a sector of angle P (in degree) of a circle with radius R is : [SEBA 2015]

(a) (b) (c) (d)

Solution: (d)

Q2. 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)

Q3. 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 ,

]

Q4. 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 ]

Q5. 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

]

Q6. 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

]

Q7. 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)

Q8. 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)

Q9. 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)

Q10. 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

]

Q11. In the given figure , if the angle 30° , then the area of the shaded region (in cm square) is : [CBSE 2011]

(a) 3.36 (b) 2.26 (c) 1.36 (d) 2.36

Solution: [ Here , cm and cm

The area of shaded region

]

Q12. 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 ]

Q13: 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 :

Q1. 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 ]

Q2. 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

]

Q3. If the diameter of a semi-circular protractor is 14 cm ,then its perimeter is . [CBSE 2009]

Solution : 22 cm .

[ Here , cm and cm

The perimeter of a semi-circular cm ]

Class 10 Areas Related to Circles Answers following the questions :

Q1. In given figure , find the area of the sector of a circle with radius 4 cm .

Solution: Here , cm and

Therefore, the area of the sector of a circle

Q2. 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

Q3. 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

Q4. The difference between the circumference and radius of a circle is 37 cm . Find the area of the circle . [ CBSE 2013]

Solution: A/Q ,

Therefore, the area of circle .

Q5. 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

Q6. 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

Q1. 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

Q2. 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 ,

Q3. 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

Q4. In figure, O be the centre of two concentric circles , cm and cm .Find the area of the shaded region .

Solution: Here , , cm and cm

Therefore, the area of the shaded region

Q5. In figure, OABC is a quadrant of a circle with centre O and radius 3.5 cm . If cm ,find the area of shaded region .

Solution: Here , cm and cm

Therefore, the area of shaded region

Q6. 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

Class 10 Areas Related to Circles 3 Marks Questions and Answers

SECTION = C

Q1. 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) Area of major sector

Q2. 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

Class 10 Areas Related to Circles 4 Marks Questions and Solutions

SECTION = D

Q1. In figure, a square OPQR is inscribe in a quadrant OAQB of a circle. If the radius of the circle is cm , find the area of the shaded region . [Use π = 3.14] [CBSE 2020 standard]

Solution: Given, be a square .

So , cm

Area of square

In , we have

Radius cm

Area of the quadrant

Therefore, the area of shaded region

Q3. In figure , ABCD is a square with side cm and inscribed in a circle .Find the area of the shaded region . [Use ] [CBSE 2019]

Solution: Given cm and We join AC .

InABC , we have

Radius

Therefore, the area of the shaded region Area of circle – Area of ABCD

Q4. Find the area of the shaded design in figure, where ABCD is a square of side 10 cm and semicircles are drawn with each side of the square as diameter . [ Use ]

Solution: Here , cm , Radius cm

Area of unshaded region part and part

Area of ABCD Area of two semicircle

Area of unshaded region part and part .

Therefore, the area of shaded design

Area of square ABCD Area of

Q5. Calculate the area of the designed region in figure ,common between the two quadrants of circles of radius 8 cm each . [CBSE 2012]

Solution: The radius of the quadrant of a circle cm

And the side of the square cm

Therefore, the area of the shaded region

Area of two quadrant of the circle – Area of the square

Q6. In figure , a square OABC is inscribed in a quadrant OPBQ .If OA = 15 cm , find the area of the shaded region . [ Use ] [CBSE 2019]

Solution: Since OABC is a square .

So , cm and we join OB .

In OAB we have ,

Radius cm

Therefore , the area of shaded region

Area of quadrant of the circle – Area of square OABC

Class 10 Areas Related to Circles 4 or 5 Marks QuestionsSolutions

SECTION = E

Q1. In figure, AB and CD are two diameter of a circle (with centre) perpendicular to each other and OD is the diameter of the smallest circle . If , find the area of the shaded region . [CBSE 2013,2020 Basic]

Solution: For big circle : Radius cm ,

Diameter cm

So, cm

For small circle : Diameter cm

and Radius cm

Area of small circle

Area of

Area of semicircle

The area of the shaded region

Area of small circle Area of semicircle –

Q2. In figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter . Find the area of the shaded region . [CBSE 2014]

Solution: For ABCD quadrant :

Here , Radius cm

In∆ABC , we have

area of

And Area of quadrant ABCD

For semi-circle BEC :

Diameter cm ; Radius cm

Area of semi-circle BEC

Area of shaded region ar() ar(semicircle BEC) – ar(quadrant ABCD)

Q3. In figure, ABC is a right angled triangle in which , cm and cm , then the semi-circles are described on AB , BC and AC as diameters . Find the area of the shaded region .

Solution: Here , cm and cm

In ABC , we have

The radius of three semicircle are : cm ; cm

And cm

Therefore, the area of the shaded region

Area of semicircle with diameter AB Area of triangle ABC

Area of semicircle with diameter AC Area of semicircle with diameter BC