### Assertion & Reason Questions For Math Class 10 | Arithmetic Progression

Top of Form ASSERTION & REASON QUESTIONS CLASS 10  CHAPTER 1  REAL NUMBERS Competency based questions on ARITHMETIC PROGRESSION chapter 5 , Assertion and Reason based questions for class 10 ARITHMETIC PROGRESSION chapter 5

MATHEMATICS

# 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 :
$r=\frac{Area\: of \: sector}{Length\: of\: arc}$
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  = $\frac{Difference\: of\: two\: areas}{Origional Area}\times 100$

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 = $\frac{1}{2}$(2r + 20% of 2r)

Find the difference of two areas

Required Percentage  = $\frac{Difference\: of\: two\: areas}{Origional Area}\times 100$
Q 42)  Find the area swept by minute hand of length 12 cm in 20 minutes.

$a)\: \: \: \frac{956}{7}cm^{2}$

$b)\: \: \: \frac{1056}{7}cm^{2}$

$c)\: \: \: \frac{1046}{7}cm^{2}$

$d)\: \: \: \frac{1038}{7}cm^{2}$

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 $\pi$ cm2

b) 18 $\pi$ cm2

c) 12$\pi$ cm2

d) 9$\pi$ 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 2021-22Basic 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 = $\frac{1}{2}$ 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