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

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__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

Q 2) What is the formula for the area of a circle?

a) A = πd

^{2}

b) A = πs

^{2}

c) A = πr

^{2}

d) A = πa

^{2}

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

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

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

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

Q 7) Find the area of the circle whose circumference is 44 cm.

a) 154 cm

^{2}

b) 308 cm

^{2}

c) 77 cm

^{2}

d) 231 cm

^{2}

a) 1.35 m

b) 6.54 m

c) 18.00 m

d) 8.05 m

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

(a) r

^{2}

(b) 1/2r

^{2}

(c) 2r

^{2}

(d) √2r

^{2}

Ans: a

a) √0.83 m

b) 5 m

c) √0.63 m

d) √38 m

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

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

Q 14) The area of the circle that can be inscribed in a square of side 8 cm is

(a) 36 π cm

^{2}

(b) 16 π cm

^{2}

(c) 12 π cm

^{2}

(d) 9 π cm

^{2}

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 cm

^{2}

(a) 256 cm

^{2}

(b) 128 cm

^{2}

(c) 642 cm

^{2}

(d) 64 cm

^{2}

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

16

^{2}= a

^{2}+ a

^{2}⇒ 256 = 2a

^{2}⇒ a

^{2}= 256/2 ⇒ a

^{2}= 128 = Area of a Square

(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 r

^{2}

∴ Area of the sector with angle 60° = (60°/360°) × π r

^{2}cm

^{2}= (36/6) π cm

^{2}= 6 × (22/7) cm

^{2}= 132/7 cm

^{2}

a) Large

b) Major

c) Big

d) Wide

Q 18) What is the name of the sector with a smaller area?

a) Small

b) Narrow

c) Minor

d) Tiny

Q 19) Number of sectors in a circle are ____

a) 2

b) 3

c) 4

d) 1

Ans: a

Solution Hint

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

a) 0.07 m

b) 0.47 cm

c) 0.79 m

d) 0.57 cm

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 cm

^{2}

(b) 220 cm

^{2}

(c) 231 cm

^{2}

(d) 250 cm

^{2}

Ans: c

(a) p/180 × 2πR

(b) p/180 × π R

^{2}

(c) p/360 × 2πR

(d) p/720 × 2πR

^{2}

Ans: d

Q 24) If the area of a circle is 154 cm

^{2}, then its perimeter is

(b) 22 cm

(c) 44 cm

(d) 55 cm

Ans: c

Solution Hint

Given, Area of a circle = 154 cm

^{2}

πr

^{2}= 154 ⇒ (22/7) × r

^{2}= 154

^{2}= (154 × 7)/22 ⇒ r

^{2}= 7 × 7 ⇒ r = 7 cm Perimeter of circle = 2πr = 2 × (22/7) × 7 = 44 cm

(a) (πr

^{2}θ)/360

^{2}θ)/180

(d) (2πrθ)/180

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

(a) 56 cm

(b) 42 cm

(c) 28 cm

(d) 16 cm

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

(a) 441 cm

^{2}

(b) 462 cm

^{2}

(c) 386 cm

^{2}

(d) 512 cm

^{2}

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

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

Q 31) The area of a quadrant of a circle with circumference of 22 cm is

(a) 77 cm

^{2}

(b) 77/8 cm

^{2}

(b) 35.5 cm

^{2}

(c) 77/2 cm

^{2}

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

(a) 44 cm

(b) 28 cm

(c) 11 cm

(d) 22/3 cm

^{2}. 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 cm

^{2}

b) 184 cm

^{2}

c) 154 cm

^{2}

d) 259 cm

^{2}

a) 3.07 m

b) 2.74 m

c) 2.33 m

d) 4.57 m

a) 54 m

b) 27m

c) 42 m

d) 56 m

Ans: a

Solution Hint

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

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

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

Ans: b

a)
42 cm^{2}

b)
48 cm^{2}

c)
38.5 cm^{2}

d)
77 cm^{2}

a)
54 cm^{2}

b)
42 cm^{2}

c)
48 cm^{2}

d)
36 cm^{2}

a)
16.3 cm^{2}

b)
17.3 cm^{2}

c)
18.8 cm^{2}

d)
18.3 cm^{2}

^{2}

b)
231 cm^{2}

c)
308 cm^{2}

d)
316 cm^{2}

a) 54 cm^{2}

b)
42 cm^{2}

c)
56 cm^{2}

d)
48 cm^{2}

^{2}

b)
1416 cm^{2}

c)
1308 cm^{2}

d)
1386 cm^{2}

^{2}

b)
154 cm^{2}

c)
308 cm^{2}

d)
77 cm^{2}

a)
36 cm^{2}

b)
18 cm^{2}

c)
12 cm^{2}

d)
9 cm^{2}

a)
256 cm^{2}

b)
128 cm^{2}

c)
64 cm^{2}

d)
77 cm^{2}

**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

(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

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 ̊

**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

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

^{2}

(b)
49 cm^{2}

(c)
98 cm^{2}

(d)
49π/2 cm^{2}

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)

^{2}

^{}

(b)
(π/6 - √3/4) cm^{2}

(c)
4(π/6 - √3/4) cm^{2}

(d)
8(π/6 - √3/4) cm^{2}

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°

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### Comments

Very nice

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