CBSE Class 10 Mathematics Areas related to circles MCQs Set 01

Practice MCQs for Class 10 Mathematics Chapter 11 Areas Related to Circles

Access targeted multiple-choice questions for Chapter 11 Areas Related to Circles designed to align with the latest CBSE academic syllabus for Class 10 Mathematics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

Access Chapter 11 Areas Related to Circles Questions and Solutions

Access the complete set of multiple-choice questions for Chapter 11 Areas Related to Circles below. This focused format allows students to isolate specific topics for thorough review and uninterrupted practice alongside official CBSE textbooks.

Question : If 2/x + 3/y = 13 and 5/x - 4/y = - 2, then x + y equals
(a) 1/6
(b) −1/6
(c) 5/6
(d) −5/6
Answer : C

Question : Equation 5/x -1 + 1/y − 2 = 2 is reduced in linear equation as 5p + q = 2. Then the values of p and q respectively are
(a) 1/x - 1, 1/y − 2
(b) 1/y - 1, 1/x - 2
(c) x – 1, y – 2
(d) x + 1, y + 2
Answer : A

Question : If 2/x + 3/y = 13 and 5/x - 4/y = - 2, then the values of x and y respectively are
(a) 1/2, 1/3
(b) 1/3, 1/4
(c) 1/2, 1/5
(d) 2, 3
Answer : A

Question : 1/3x + y + 1/3x - y = 3/4 and 1/2(3x + y) - 1/2(3x - y) = −1/8, where 3x + y ≠ 0, 3x – y ≠ 0, then
(a) 1, 2
(b) 1, 1
(c) 1, 3
(d) 1, 4
Answer : B

Question : If 2/x + 2y = 15 and 2/x − 4y = 3, then the values of x and y, respectively are
(a) 2/11, 2
(b) 3, 1/3
(c) 4, 1/4
(d) 1/4, 4
Answer : A

Question : If 1/x = u and 1/y = v, then 2/x + 3/y = 13 becomes
(a) 3u + 2v = 13
(b) 2u + 3v = 13
(c) 2/u + 3/v = 13
(d) 2/v + 3/u = 13
Answer : B

Question : If 3a/x - 2b/y + 5 = 0 and a/x + 3b/y – 2 = 0, then
(a) x = 1/a, y = 1/b
(b) x = 1/b, y = 1/a
(c) x – a, y = b
(d) x = a, y = – b
Answer : C

Question : Area of the largest triangle inscribed in a semi-circle of radius r units is
(a.) r2 sq. units
(b.) (1/2) r2 sq. units
(c.) 2r2 sq. units
(d.) √2 r2 sq. units
Answer : A

Question : Radii of two circles are 4 cm and 3 cm respectively. There is another circle, which is having area equal to the sum of the areas of two circles whose radii are known. Find the diameter (in cm) of the third circle.
(a.) 5
(b.) 7
(c.) 0
(d.) 14
Answer : C

Question : If 1/2x - 1/y = – 1 and 1/x + 1/2y = 8, (x ≠ 0, y ≠ 0), then
(a) x = 1/4 , y = 1/2
(b) x = 1/3, y = 1/5
(c) x = 1/6, y = 1/8
(d) x = 1/6, y = 1/4
Answer : D

Question : The area of the quadrant of a circle of radius r is :
(a) 1/2πr2
(b) 1/2πr
(c) 1/4πr2
(d) (π/2+2r)
Answer : C

Question : If θ is the angle in degrees of a sector of a circle of radius r units, then the area of the sector is
(a.) Πr2θ/360
(b.) πr2θ/180
(c.) 2πrθ/360
(d.) 2πrθ/180
Answer : A

Question : Which ratio is denoted by a constant known as π
(a.) 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟/𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒
(b.) 𝐴𝑟𝑒𝑎/𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒
(c.) 𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒/𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟
(d.) 𝐴𝑟𝑒𝑎/𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟
Answer : C

Question : If the circumference of a circle and the perimeter of a square are equal, then the
(a.) Area of the circle = Area of the square
(b.) Area of the circle > Area of the square
(c.) Area of the circle < Area of the square
(d.) We cannot definitely say about the relation between area of the circle and the square
Answer : B

Question : Find area of the largest circle that can be drawn inside a rectangle with length a cm and breadth b cm. (a > b).
(a.) 𝑎2𝜋/4 cm2
(b.) 𝑏2𝜋/2 cm2
(c.) 𝑏2𝜋/4 cm2
(d.) 𝑎2𝜋/2 cm2
Answer : B

Question : The ratio of areas of two circles whose ratio of circumferences is in the ratio of 3 : 1 will be
(a.) 3 : 1
(b.) 1 : 3
(c.) 1 : 9
(d.) 9 : 1
Answer : D

Question : Area of a square is same as area of a circle. What will be the ratio of their perimeters?
(a.) 1 : 1
(b.) π : √2
(c.) 2 : √𝜋
(d.) None of these
Answer : C

Question : The minute hand of a clock is 14 cm long . The area described by it on the face of the clock in 5 minutes is
(a.) 51.33 cm2
(b.) 15.33 cm2
(c.) 21.15 cm2
(d.) 12.35 cm2
Answer : A

Question : A display board is in the shape of a circle. While designing the board, if diameter of the board is increased by 40% from the previous design, then the area will be increased by
(a.) 40%
(b.) 80%
(c.) 96%
(d.) 45%
Answer : C

Question : If the circumference of a circle is 44 cm, then the area of a circle is
(a) 276 cm2 
(b) 44 cm2 
(c) 176 cm2 
(d) 154 cm2
Answer : D
 
Question : Area of a quadrant of a circle of circumference 22 cm, is :
(a) 3.05 cm2 
(b) 3.5 cm2 
(c) 9.625 cm2 
(d) 35.5 cm2
Answer : C
 
Question : If the circumference of a circle is equal to the perimeter of a square, then the ratio of their areas is :
(a) 22 : 7 
(b) 14 : 11 
(c) 7 : 22 
(d) 7 : 1
Answer : B
 
Question : The area of the largest circle that can be drawn inside a rectangle with sides 7 m × 3.5 m is :
(a) 77/2 m2
(b) 77 cm2 
(c) 77/8 m2
(d) 77/4m2
Answer : C
 
Question : Find the perimeter of a half circle
(a) 1/2(2π r)
(b) r (2 + π) 
(c) πr /2
(d) πr2 x 1/2
Answer : B
 
Question : In given figure, ABCD is a square of 14 cm, find the area of shaded portion, if all larger circles are equal
CBSE Class 10 Mathematics Areas related to circles MCQs Set A
(a) 57/2 (3 – 2 ) cm2 
(b) 59/3 (3 – 3 ) cm2
(c) 77/2 (3 – 2 2 ) cm2 
(d) none of these
Answer : C
 
Question : The perimeter of the following shaded portion of the figure is :
CBSE Class 10 Mathematics Areas related to circles MCQs Set A
(a) 40 m 
(b) 40. 07 m 
(c) 40. 28 m 
(d) 35 m
Answer : C
 
Question : The perimeter of a sector of a circle of radius 5.2 cm, is 16.4 cm. The area of the sector is :
(a) 31.2 cm2 
(b) 15.01 cm2 
(c) 15.6 cm2 
(d) 16.6 cm2
Answer : C
 
Question : In the adjoining figure, the larger circle with radius 4 cm is touched internally by two smaller circles which also touch each other externally at the centre O of the larger circle. The area of shaded portion is
(a) 4 π sq.units 
(b) 7 π sq.units 
(c) 12 π sq.units 
(d) 16 π sq.units
CBSE Class 10 Mathematics Areas related to circles MCQs Set A
Answer : A

Question. The area of a circular ring formed by two concentric circles whose radii are 5.7 cm and 4.3 cm respectively is (Take 𝜋=3.14)
(a) 44 sq. cm.
(b) 66 sq. cm.
(c) 22 sq. cm.
(d) 33 sq. cm
Answer : A

Question.The area of a circle is 154 cm, then its diameter is
(a) 7𝑐𝑚
(b) 21𝑐𝑚
(c) 40𝑐𝑚
(d) 28𝑐𝑚
Answer : C

Question. The diameter of a wheel is 40 cm. How many revolutions will it make on covering 176 m ?
(a) 140
(b) 150
(c) 160
(d) 166
Answer : A

Question. The perimeter of circular field is 242 cm. The area of the field is :-
(a) 9317 cm2
(b)18634 cm2
(c) 4658.5 cm2
(d) None of these
Answer : C

Question. The diameter of a wheel is 1.26 metres. How long will it travel in 500 revolutions?
(a) 1492
(b) 2530
(c) 1980
(d) 2880
Answer : C

Question. The difference between the circumference and radius of a circle is 37 cm. The area of the circle is:-
(a) 111cm2
(b) 184 cm2
(c) 154 cm2
(d) 259 cm2
Answer : C

 

CASE STUDY QUESTION 

Q1. Pookalam is the flower bed or flower pattern designed during Onam in Kerala. It is similar as Rangoli in North India and Kolam in Tamil Nadu. During the festival of Onam, your school is planning to conduct a Pookalam competition. Your friend who is a partner in competition, suggests two designs given below.

Observe these carefully.

""CBSE-Class-10-Mathematics-Area-Related-To-Circle-4

Design I: This design is made with a circle of radius 32cm leaving equilateral triangle ABC in the middle as shown in the given figure.
Design II: This Pookalam is made with 9 circular design each of radius 7cm.

Refer Design I:

Question : Find the side of equilateral triangle is
Answer : 32√3 cm

Question : Find the altitude of the equilateral triangle is
Answer : 48cm

Refer Design II:

Question : Find the area of square is
Answer : 1764 m2

 

Q2. In figure, O is the centre of a circle such that diameter AB = 13 cm and AC = 12 cm. BC is joined. Find the area of the shaded region.

""CBSE-Class-10-Mathematics-Area-Related-To-Circle-5

Question : Find the perimeter of circle.
Answer : 40.85 cm

Question : Find the area of triangle.
Answer : 30 cm²

Question : Find the area of shaded portion.
Answer : 36.33 cm²

 

Question : The area of a circle is 49 πcm2. Its circumference is
(a) 7π cm
(b) 14π cm
(c) 21π cm
(d) 28π cm

Question : The perimeter of circular field is 242cm. The area of the field is
(a) 9317 cm2
(b) 18634 cm2
(c) 4658.5 cm2
(d) none of these

Question : The area of a circle is 38.5 cm2. Its circumference is
(a) 62 cm
(b) 12.1 cm
(c) 11 cm
(d) 22 cm

Question : The difference between the circumference and radius of a circle is 37 cm. The area of the circle is
(a) 111 cm2
(b) 184 cm2
(c) 154 cm2
(d) 259 cm2

Question : The circumference of two circles are in the ratio 2 : 3. The ratio of their areas is
(a) 2 : 3
(b) 4 : 9
(c) 9 : 4
(d) none of these

Question : On increasing the diameter of circle by 40%, its area will be increased by
(a) 40%
(b) 80%
(c) 96%
(d) none of these

Question : On decreasing the radius of the circle by 30%, its area is decreased by
(a) 30%
(b) 60%
(c) 45%
(d) none of these

Question : The area of the square is the same as the area of the circle. Their perimeter re in the ratio
(a) 1 : 1
(b) π : 2
(c) 2 : π 
(d) none of these

Question : The areas of the two circle are in the ratio 4 : 9. The ratio of their circumference is
(a) 2 : 3
(b) 4 : 9
(c) 9 : 4
(d) 4 : 9

Question : In making 1000 revolutions, a wheel covers 88 km. The diameter of the wheel is
(a) 14 m
(b) 24 m
(c) 28 m
(d) 40 m

Question : The diameter of a wheel is 40 cm. How many revolutions will it make an covering 176 m?
(a) 140
(b) 150
(c) 160
(d) 166

Question : The radius of wheel is 0.25 m. How many revolutions will it make in covering 11 km?
(a) 2800
(b) 4000
(c) 5500
(d) 7000

Question : Find the circumference of a circle of diameter 21 cm.
(a) 62 cm
(b) 64 cm
(c) 66 cm
(d) 68 cm

Question : Find the area of a circle whose circumference is 52.8 cm.
(a) 221.76 cm2
(b) 220.76 cm2
(c) 200.76 cm2
(d) none of these.

Question : A steel wire when bent in the form of a square, encloses an area of 121 sq. cm. The same wire is bent in the form of a circle. Find the area of the circle.
(a) 111 cm2
(b) 184 cm2
(c) 154 cm2
(d) 259 cm2

Question : A wire is looped in the form of a circle of radius 28 cm. It is rebent into a square form. Determine the length of the side of the square.
(a) 42 cm
(b) 44 cm
(c) 46 cm
(d) 48 cm

Question : A circular part, 42 m in diameter has a path 3.5 m wide running round it on the outside. Find the cost of gravelling the path at Rs. 4 per m2.
(a) Rs. 2800
(b) Rs. 2020
(c) Rs. 2002
(d) none of these

Question : A road which is 7m wide surrounds a circular park whose circumference is 352 m. Find the area of the road.
(a) 2618 m2
(b) 2518 m2
(c) 1618 m2
(d) none of these

Question : If the perimeter of a semicircular protractor is 36 cm, find the diameter.
(a) 14 cm
(b) 16 cm
(c) 18 cm
(d) 12 cm

Question : A bicycle wheel makes 5000 revolutions in moving 11 km. Find the diameter of the wheel.
(a) 60 cm
(b) 70 cm
(c) 66 cm
(d) 68 cm

Question : The diameter of the wheels of a bus is 140 cm. How many revolutions per minute must a wheel make in order to move a t a speed of 66km/hr
(a) 240
(b) 250
(c) 260
(d) 270

Question : A paper is in the form of a rectangle ABCD in which AB = 18cm and BC = 14cm. A semicircular portion with BC as diameter is cut off. Find the area of the remaining paper (see in below figure).

class_10_maths_mcq_017

(a) 175 cm2
(b) 165 cm2
(c) 145 cm2
(d) none of these

Question : Find the area of the shaded region in the above sided figure. Take π = 3.14
(a) 75 cm2
(b) 72 cm2
(c) 70 cm2
(d) none of these

Question : A square ABCD is inscribed in a circle of radius ‘r’. Find the area of the square in sq. units.
(a) 3r2
(b) 2r2
(c) 4r2
(d) none of these

Question : Find the area of a right-angled triangle, if the radius of its circumcircle is 2.5 cm and the altitudedrawn to the hypotenuse is 2 cm long.
(a) 5 cm2
(b) 6 cm2
(c) 7 cm2
(d) none of these

Question : The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm. Find the area of the sector.
(a) 44 cm2
(b) 44.6 cm2
(c) 44.8 cm2
(d) none of these

Question : The minute hand of a clock is 12 cm long. Find the area of the face of the clock described by the minute hand in 35 minutes.
(a) 265 cm2
(b) 266 cm2
(c) 264 cm2
(d) none of these

Question : Find the area of the shaded region in the given figure, if Pr = 24 cm, PQ = 7 cm and O is the centre of the circle.

class_10_maths_mcq_016

(a) 164.54 cm2
(b) 161.54 cm2
(c) 162.54 cm2
(d) none of these

Question : In the above-sided figure, AB is a diameter of a circle with centre O and OA = 7 cm. Find the area of the shaded region.
(a) 64.5 cm2
(b) 61.5 cm2
(c) 66.5 cm2
(d) none of these

Question : A racetrack is in the form of a ring whose inner circumference is 352 m and outer circumference is 396 m. Find the width of the track.
(a) 4 m
(b) 6 m
(c) 8 m
(d) 7 m

Question : The difference between the circumference and the radius of a circle is 37 cm. Find the area of the circle.
(a) 111 cm2
(b) 184 cm2
(c) 154 cm2
(d) 259 cm2

Question : The circumference of a circle exceeds its diameter by 16.8 cm. Find the circumference of the circle.
(a) 24.64 cm
(b) 26.64 cm
(c) 28.64 cm
(d) 22 cm

Question : A copper wire when bent in the form of square encloses an area of 484 cm2. The same wire is now bent in the form of a circle. Find the area of the circle.
(a) 116 cm2
(b) 166 cm2
(c) 616 cm2
(d) none of these

Question : Find the area of the sector of a circle of radius 14 cm with central angle 450.
(a) 76 cm2
(b) 77 cm2
(c) 66 cm2
(d) none of these

Question : A sector is cut from a circle of radius 21 cm. The angle of the sector is 1500. Find the length of the arc.
(a) 56 cm
(b) 57 cm
(c) 55 cm
(d) 58 cm

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Practice MCQs for Class 10 Mathematics Chapter 11 Areas Related to Circles

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