Maths MCQ Ch-12 Class 10 | Area Related to Circle

  MATHEMATICS

MCQ | CHAPTER 12 | CLASS 10

Area Related to the Circles

Q 1) What is the formula for the circumference of a circle?
a) C = 2πd
b) C = 2πr
c) C = 2πa
d) C = 2πs 

Ans: b

Q 2) What is the formula for the area of a circle?
a) A = πd²
b) A = πs²
c) A = πr²
d) A = πa²

Ans: c

Q 3) The circumference of the circle having diameter 8.4 cm is
a) 25.2 cm
b) 26.4 cm
c) 28 cm
d) 27.6 

Ans: b

Q 4) The perimeter of a circle having radius 5cm is equal to:
(a) 30 cm
(b) 3.14 cm
(c) 31.4 cm
(d) 40 cm 

Ans: c

Q 5) What is the circumference of a circle if the radius is 7 m?
a) 8 m
b) 2 m
c) 44 m
d) 22 m 

Ans: c

Q 6) Area of the circle with radius 5cm is equal to:
(a) 60 sq.cm
(b) 75.5 sq.cm
(c) 78.5 sq.cm
(d) 10.5 sq.cm 

Ans: c
Q 7) Find the area of the circle whose circumference is 44 cm.
a) 154 cm²
b) 308 cm²
c) 77 cm²
d) 231 cm² 

Ans: a

Q 8) Find the area of a semicircle if the radius is 6 cm.
a) 1.35 m
b) 6.54 m
c) 18.00 m
d) 8.05 m 

Ans: b

Q 9) Find the radius of the circle if the circumference is 12 m.
a) 1.90 m
b) 1.09 m
c) 7.90 m
d) 1.40 m
Ans: a

Q 10) The largest triangle inscribed in a semi-circle of radius r, then the area of that triangle is;

(a) r²

(b) 1/2r²

(c) 2r²

(d) √2r²
Ans: a

  Q 11) Find the radius of a circle if 2 m is the area of the circle.
a) √0.83 m
b) 5 m
c) √0.63 m
d) √38 m 

Ans: c

Q 12) If the perimeter of the circle and square are equal, then the ratio of their areas will be equal to:
(a) 14:11
(b) 22:7
(c) 7:22
(d) 11:14 

Ans: a

Q 13) The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameter 36 cm and 20 cm is
a) 28 cm
b) 42 cm
c) 56 cm
d) 16 cm 

Ans: a

Q 14) The area of the circle that can be inscribed in a square of side 8 cm is
(a) 36 π cm²
(b) 16 π cm²
(c) 12 π cm²
(d) 9 π cm²
Ans: b
Solution Hint
Given, Side of square = 8 cm
Diameter of a circle = side of square = 8 cm
Therefore, Radius of circle = 4 cm Area of circle = π(4)²  = 16π cm²

Q 15) The area of the square that can be inscribed in a circle of radius 8 cm is

(a) 256 cm²

(b) 128 cm²

(c) 642 cm²

(d) 64 cm²

Ans: b

Solution Hint

Radius of circle = 8 cm

Diameter of circle = 16 cm = diagonal of the square

Let “a” be the triangle side, and the hypotenuse is 16 cm

Using Pythagoras theorem, we can write

16² = a² + a² ⇒ 256 = 2a² ⇒ a² = 256/2 ⇒ a² = 128 = Area of a Square

Q 16) The area of a sector of a circle with radius 6 cm if the angle of the sector is 60°.
(a) 142/7
(b) 152/7
(c) 132/7
(d) 122/7
Ans: c
Solution Hint
Angle of the sector is 60°
Area of sector = (θ/360°) × π r²
∴ Area of the sector with angle 60° = (60°/360°) × π r² cm²= (36/6) π cm² = 6 × (22/7) cm² = 132/7 cm²

Q 17) What is the name of the sector with a larger area?
a) Large
b) Major
c) Big
d) Wide 

Ans: b

Q 18) What is the name of the sector with a smaller area?
a) Small
b) Narrow
c) Minor
d) Tiny 

Ans: c

Q 19) Number of sectors in a circle are ____
a) 2
b) 3
c) 4
d) 1
Ans: a
Solution Hint 

A circle contains two sectors. The sector having a larger area is called a major sector and the sector having a smaller area is called a minor sector.

Q 20) In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. The length of the arc is;
(a) 20cm
(b) 21cm
(c) 22cm
(d) 25cm 

Ans: c

Q 21) Find the radius of the wheel if the wheel rotates 100 times to cover 500 m.
a) 0.07 m
b) 0.47 cm
c) 0.79 m
d) 0.57 cm 

Ans: c

Q 22) In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. The area of the sector formed by the arc is:
(a) 200 cm²
(b) 220 cm²
(c) 231 cm²
(d) 250 cm²
Ans: c

Q 23) Area of a sector of angle p (in degrees) of a circle with radius R is
(a) p/180 × 2πR
(b) p/180 × π R²
(c) p/360 × 2πR
(d) p/720 × 2πR²
Ans: d

 
Q 24) If the area of a circle is 154 cm², then its perimeter is

(a) 11 cm
(b) 22 cm
(c) 44 cm
(d) 55 cm
Ans: c
Solution Hint
Given, Area of a circle = 154 cm²
πr² = 154   ⇒ (22/7) × r² = 154

r² = (154 × 7)/22 ⇒ r² = 7 × 7 ⇒ r = 7 cm Perimeter of circle = 2πr = 2 × (22/7) × 7 = 44 cm

Q 25) If θ is the angle (in degrees) of a sector of a circle of radius r, then the length of arc is
(a) (πr²θ)/360

(b) (πr²θ)/180

(c) (2πrθ)/360
(d) (2πrθ)/180 

Ans: c

Q 26) It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would be
(a) 10 m
(b) 15 m
(c) 20 m
(d) 24 m
Ans: a

Q 27) The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is
(a) 56 cm
(b) 42 cm
(c) 28 cm
(d) 16 cm 

Ans: c

Q 28) Find the area of a sector of circle of radius 21 cm and central angle 120°.
(a) 441 cm²

(b) 462 cm²

(c) 386 cm²

(d) 512 cm²
Ans: b

 
Q 29) The wheel of a motorcycle is of radius 35 cm. The number of revolutions per minute must the wheel make so as to keep a speed of 66 km/hr will be
(a) 50
(b) 100
(c) 500
(d) 1000
Ans: c
Solution Hint
Circumference of the wheel = 2πr = 2 × (22/7) × 35 = 220 cm
Speed of the wheel = 66 km/hr = (66 × 1000)/60 m/min
= 1100 × 100 cm/min = 110000 cm/min 

Number of revolutions in 1 min = 110000/220 = 500

Q 30) If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
(a) 2 units
(b) π units
(c) 4 units
(d) 7 units 

Ans: a

Q 31) The area of a quadrant of a circle with circumference of 22 cm is
(a) 77 cm²
(b) 77/8 cm²
(b) 35.5 cm²
(c) 77/2 cm² 

Ans: b

Q 32) A chord of a circle of radius 10 cm subtends a right at the centre. Find length of the arc.
a) 16.7 cm
b) 15.7 cm
c) 15.2 cm
d) 14.7 cm 

Ans: b

Q 33) In a circle of radius 14 cm, an arc subtends an angle of 30° at the centre, the length of the arc is
(a) 44 cm
(b) 28 cm
(c) 11 cm
(d) 22/3 cm 

Ans: d

Q 34) An arc of a circle is of length 6π cm and the area of the sector is 21π cm². Find the diameter.

a) 14 cm

b) 7 cm

c) 21 cm

d) 10.5 cm

Ans: a

Solution Hint Find the radius by using the relation :

Q 35) The difference between circumference and diameter of a ring is 10 cm. Find the radius of the ring.
a) 3.07 cm
b) 0.37 cm
c) 2.33 cm
d) 4.57 cm
Ans: c

Solution Hint Circumference – Diameter = 10 cm (∵ Diameter = 2 × radius)
2πr – 2r = 10 cm ⇒ 2r(π – 1) = 10 cm
Q 36) The difference between the circumference and radius of a circle is 37 cm then area of the circle is
a) 111 cm²
b) 184 cm²
c) 154 cm²
d) 259 cm² 

Ans: c

Q 37) Find the diameter of the circle if the area of the circle is 6 m.
a) 3.07 m
b) 2.74 m
c) 2.33 m
d) 4.57 m 

Ans: b

Q 38) If the diameter of the semi-circular plot is 21 cm, then its perimeter is
a) 54 m
b) 27m
c) 42 m
d) 56 m
Ans: a

Solution Hint 

Perimeter of semi- circle is : πr + 2r
Q 39) Ratio of areas of two circles is 9 : 16. Find the ratio of their circumferences.
a) 9 : 16
b) 3 : 4
c) 16 : 9
d) 4 : 3 

Ans: b

Q 40) If radius of a circle is increased by 20 % then its area will be increased by
a) 40 %
b) 42 %
c) 44 %
d) 45 %
Ans: c
Solution Hint
Find area by taking radius r
Find new area by taking radius = r + 20% of r

Find the difference of two areas

Required Percentage  = 

Q 41)  If diameter of a circle is decreased by 10 %  then its area will be decreased by

a) 20 %                                                      

b) 18 %

c) 19 %                                                      

d) 11 %

Ans: c

Solution Hint

Take diameter = 2r and radius = r

Find area by taking radius r

Find new area by taking radius = (2r + 20% of 2r)

Find the difference of two areas

Required Percentage  = 

Q 42)  Find the area swept by minute hand of length 12 cm in 20 minutes.

  

  

  

Ans: b

Q 43)  Find the area of the shaded part

a) 42 cm²     

b) 48  cm²         

c) 38.5 cm²          

d) 77 cm²

Ans: c

Q 44)  Find shaded area if ABCD is a square of side 14 cm and APD and BPC are semi circle 

a) 54 cm²                                                         

b) 42  cm²         

c) 48 cm²                                                         

d) 36 cm²

Ans: b

Q 45)  A square of diagonal   8 cm is inscribed in a circle. Find the shaded area.

a) 16.3 cm²                                                         

b) 17.3  cm²         

c) 18.8 cm²                                                         

d) 18.3 cm²

Ans: d

Q 46)  Arcs have been drawn with radii 14 cm each and with centre P, Q, R. Find the shaded region.

a) 154 cm²                                                           

b) 231  cm²         

c) 308 cm²                                                           

d) 316 cm²

Ans: c

Q 47)  In a square of side 14 cm, four equal circles are  drawn. Find the area of the shaded region.

a) 54 cm² 

b) 42  cm²         

c) 56 cm²

d) 48 cm²

Ans: b

Q 48)  ABCD is a quadrilateral, arcs have been drawn of radii 21 cm each with vertices A, B, C, D. Find the shaded area.

a) 1396 cm²                                                          

b) 1416  cm²         

c) 1308 cm²                                                          

d) 1386 cm²

Ans: d

Q 49)  In a rectangle 22 cm X 14 cm, a semi circle is drawn with 14 cm as diameter. Find the shaded area.

a) 231 cm²                                                        

b) 154  cm²         

c) 308 cm²                                                        

d) 77 cm²

Ans: a

Q 50)  Find the area of the circle that can be inscribed in a square of side 6 cm

a) 36  cm²                                                      

b) 18  cm²         

c) 12 cm²                                                      

d) 9 cm²

Ans: d

Q 51)  Find the area of the square that can be inscribed in a circle  of radius 8 cm

a) 256 cm²                                                        

b) 128  cm²         

c) 64 cm²                                                           

d) 77 cm²

Ans: b

Questions from CBSE Sample paper 2021-22
Basic Mathematics (241)

Q 52) In a circle of diameter 42cm ,if an arc subtends an angle of 60 ̊ at the centre where 𝜋 = 22/7,then the length of the arc is
(a) 22/7 cm
(b) 11cm
(c) 22 cm

(d) 44 cm
Ans: c

Q 53) If the circumference of a circle increases from 2𝜋 to 4𝜋 then its area _____ the original area
(a) Half
(b) Double
(c) Three times
(d) Four times
Ans: d

Q 54) If the difference between the circumference and the radius of a circle is 37cm , 𝜋 = 22/7, the circumference (in cm) of the circle is
(a) 154
(b) 44
(c) 14
(d) 7
Ans: b

Q 55) The perimeter of a semicircular protractor whose radius is ‘r’ is
(a) 𝜋 + 2r
(b) 𝜋 + r
(c) 𝜋 r
(d) 𝜋 r + 2r
Ans: d

Solution Hint
Perimeter of protractor = Circumference of semi-circle + 2 x radius = 𝜋 r + 2r

Q 56)  Area of a sector of a circle is 1/6 to the area of circle. Find the degree measure of its minor arc.

(a) 90 ̊                                           

(b) 60 ̊

(c) 45 ̊                                           

(d) 30 ̊

Ans: b

Standard Maths SPQ (041)

Q 57)  The number of revolutions made by a circular wheel of radius 0.7m in rolling a distance of 176m is

(a) 22                                                 

(b) 24

(c) 75                                                 

(d) 40

Ans: d
Q 58)  In the figure given below, ABCD is a square of side 14 cm with E, F, G and H as the mid points of sides AB, BC, CD and DA respectively. The area of the shaded portion is

(a) 44cm²                                           

(b) 49 cm²

(c) 98 cm²                                          

(d) 49π/2 cm²

Ans: c

Solution Hint

Shaded area = Area of semicircle + (Area of half square – Area of two quadrants)

                      = Area of semicircle + (Area of half square – Area of semicircle)

                      = Area of half square =  x 14 x14 = 98cm²

Q 59)  Given below is the picture of the Olympic rings made by taking five congruent circles of radius 1cm each, intersecting in such a way that the chord formed by joining the point of intersection of two circles is also of length 1cm. Total area of all the dotted regions assuming the thickness of the rings to be negligible is

(a) 4(π/12-√3/4) cm²                          

(b) (π/6 - √3/4) cm²

(c) 4(π/6 - √3/4) cm²                          

(d) 8(π/6 - √3/4) cm²

Ans: d

Solution Hint

Let O be the  center of the circle. OA = OB = AB = 1cm.

So ∆OAB is an equilateral triangle and ∴ ∠AOB = 60°

Required Area= 8x Area of one segment with r = 1cm, θ = 60°

Q 60)  The circumference of a circle is 100 cm. The side of a square inscribed in the circle is

(a) 50√2 cm                                       

(b) 100/π cm

(c) 50√2/π cm                                   

(d) 100√2/π cm

Ans: c