CBSE Class 10 Mathematics Chapter 12 Areas Related to Circles Multiple Choice Questions with Answers. MCQ Class 10 Maths Areas Related to Circles with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Mathematics Areas Related to Circles MCQs with Answers to know their preparation level.
Multiple Choice Questions - Set - 2
Question 1:
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
Correct Answer – (D)
Given, radius = r = 14 cm
Length of arc = (2πrθ)/360
= 2 × (22/7) × 14 × (30/360)
= 22/3 cm
Question 2 :
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
Correct Answer – (A)
According to the given,
Perimeter of circle = Area of circle
2πr = πr2
⇒ r = 2
Therefore, radius = 2 units
Question 3 :
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
Correct Answer – (B)
Given, radius (r) = 21 cm
Central angle = θ = 120
Area of sector = (πr2θ)/360
= (22/7) × (21 × 21) × (120/360)
= 22 × 21
= 462 cm2
Question 4 :
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
Correct Answer – (A)
Radii of two circular parks will be:
R1 = 16/2 = 8 m
R2 = 12/2 = 6 m
Let R be the radius of the new circular park.
If the areas of two circles with radii R1 and R2 is equal to the area of circle with radius R, then
R2 = R12 + R22
= (8)2 + (6)2
= 64 + 36
= 100
R = 10 m
Question 5 :
If the sum of the areas of two circles with radii R1 and R2 is equal to the area of a circle of radius R, then
(a) R1 + R2 = R
(b) R12 + R22 = R2
(c) R1 + R2 < R
(d) R12 + R22 < R2
Correct Answer – (B)
According to the given,
πR12 + πR22 = πR2
π(R12 + R22) = πR2
R12 + R22 = R2
Question 6 :
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
Correct Answer – (B)
Given, circumference = 22 cm
2πr = 22
2 × (22/7) × r = 22
r = 7/2 cm
Area of quadrant of a circle = (1/4)πr2
= (1/4) × (22/7) × (7/2) × (7/2)
= 77/8 cm2
Question 7 :
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
Correct Answer – (C)
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
Question 8 :
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
Correct Answer – (C)
If the sum of the circumferences of two circles with radii R1 and R2 is equal to the circumference of a circle of radius R, then R1 + R2 = R.
Here,
R1 = 36/2 = 18 cm
R2 = 20/2 = 10 cm
R = R1 + R2 = 18 + 10 = 28 cm
Therefore, the radius of the required circle is 28 cm
Question 9 :
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
Correct Answer – (A)
Question 10 :
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
Correct Answer – (C)
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
