Class 10 Maths Chapter 12 Areas Related to Circles MCQ

1. The area of the circle is 154 cm2. The radius of the circle is

A. 7 cm
B. 14 cm
C. 3.5 cm
D. 17.5 cm

ANSWER= A. 7 cm Explaination: Reason: Area of circle = 154 cm² ⇒ nr² = 154 cm2 ⇒ 227 × r² = 154 ⇒ r² = 154 × 227 ⇒ r² = 7 × 7 = 49 ∴ r = √49 = 7

 

2. The area of the circle whose diameter is 21 cm is

A. 346.5 cm²
B. 37.68 cm²
C. 18.84 cm²
D. 19.84 cm²

ANSWER= A. 346.5 cm² Explaination: Reason: Here diameter = 21 cm ∴ Radius r = 212 cm Area of the circle, A = πr² ∴ A=227×212×212=11×3×212=6932=346.5cm2

 

3. The area of the sector of a circle with radius 6 cm and of angle 60° is

A. 9.42 cm²
B. 37.68 cm²
C. 18.84 cm²
D. 19.84 cm²

ANSWER= C. 18.84 cm² Explaination: Reason: Here r = 6 cm, θ = 60° Area of the sector = θ360 ∴ Area = 60360 × 3.14 × 6 × 6 = 16 × 3.14 × 6 × 6 = 3.14 × 6 = 18.84 cm²

 

4. The area of a circle is 154 cm2. Its diameter is

A. 7 cm
B. 14 cm
C. 21 cm
D. 28 cm

ANSWER= B. 14 cm Explaination: Reason: Here area of the circle, A = 154 cm², Radius, r = ? Area of the circle = 154 cm² …(Given) ∴ πr² = 154 ⇒ 227 × r² = 154 ⇒ r² = 154 × latex]\frac{7}{22}[/latex] = 7 × 7 ⇒ r = 7 cm ∴ Diameter of the circle = 2 × r = 2 × 7 = 14 cm

 

5. The length of the minute hand of a clock is 14 cm. The area swept by the minute hand in 5 minutes is

A. 153.9 cm²
B. 102.6 cm²
C. 51.3 cm²
D. 205.2 cm²

ANSWER= C. 51.3 cm² Explaination: Reason: Angle swept by the minute hand in 1 minute = (360° ÷ 60) = 6° ∴ θ = 30° ∴ Angle swept by the minute hand in 5 minutes = 6° × 5 = 30° Length of minute hand (r) = 14 cm ∴ Area swept = θ360πr² = 30360 × 227 × 14 × 14 = 1543 = 51.3 cm²

 

6. MCQ Questions For Class 10 Maths Areas Related To Circles 11. The radii of two circles are 19 cm and 9 cm respectively. The radius of the circle which has circumference equal to the sum of the circumference of two circles is

A. 35 cm
B. 10 cm
C. 21 cm
D. 28 cm

ANSWER= D. 28 cm Explaination: Reason: Let the radii of two circles be r1 and r2 and the radius of large circle be r. ∴ r1 = 19 cm, r2 = 9 cm Circumference of two circles = C1+ C2 …(where C = circle) = 2πr1 + 2πr2 = 2π × 19 + 2π × 9 = 38π + 18π = 56π ∴ Circumference of large circle = 56π ⇒ 2πr = 56π ⇒ r = 28 ∴ Radius of large circle = 28 cm

 

7. The area of the circle that can be inscribed in a square of side 6 cm, is

A. 18π cm²
B. 12π cm²
C. 9π cm²
D. 14π cm²

ANSWER= C. 9π cm² Explaination: Reason: Size of square = 6 cm, radius = 62 = 3 cm; Area of the circle = πr² = π × 3 × 3 = 9π cm²

 

8. MCQ on Area Related To Circles Class 10 14. The perimeter (in cm) of a square circumscribing a circle of radius a cm, is [AI2011]

A. 8 a
B. 4 a
C. 2 a
D. 16 a

ANSWER= A. 8 a Explaination: A. Side of a square circumscribing a circle of radius a cm = diameter of circle = 2 a cm ∴ Perimeter of the square = 4 × 2a = 8a cm

 

9. Area Related To Circle Class 10 MCQ 17. The diameter of a wheel is 1.26 m. The distance travelled in 500 revolutions is

A. 2670 m
B. 2880 m
C. 1980 m
D. 1596 m

ANSWER= C. 1980 m Explaination: C. Radius of the wheel = 1.262 = 0.63 m Distance travelled in one revolution = 2πr = 2 × 227 × 0.63 = 3.96 m ∴ Distance travelled in 500 revolutions = 500 × 3.96 = 1980 m.

 

10. If the sum of the circumferences of two circles with radii Rj and R2 is equal to the circumference of a circle of radius R, then [NCERT Exemplar Problems]

A. R1 + R2 = R
B. R1 + R2 > R
C. R1 + R2 < R
D. nothing definite can be said about the relation among Rp1, R2 and R.

ANSWER= A. R1 + R2 = R Explanation Answer: a Explaination: A. 2πR1 + 2πR2 = 2πR ⇒ R1 + R2 = R.

 

11. If 7i is taken as 227, the distance (in metres) covered by a wheel of diameter 35 cm, in one revolution, is [AI2013]

A. 2.2
B. 1.1
C. 9.625
D. 96.25

ANSWER= B. 1.1 Explaination: B. Distance covered by a wheel in one revolution = 2 πr = 2 × 227 × 352 = 110 cm = 1.1 m

 

12. A circular wire of radius 42 cm is cut and bent into the form of a rectangle whose sides are in the ratio of 6 : 5. The smaller side of the rectangle is

A. 30 cm
B. 60 cm
C. 70 cm
D. 80 cm

ANSWER= B. 60 cm Explaination: B. Length of wire = 2πrr = 2πr × 42 = 2 × 227 × 42 = 264 cm Let sides of rectangle are 6x and 5x ⇒ 2(6x + 5x) = 264 ⇒ 11x = 132 ⇒ x = 12 ∴ Smaller side = 12 × 5 = 60 cm

 

13. Perimeter of a sector of a circle whose central angle is 90° and radius 7 cm is

A. 35 cm
B. 25 cm
C. 77 cm
D. 7 cm

ANSWER= B. 25 cm

 

14. The area of a circle that can be inscribed in a square of side 10 cm is

A. 40π cm²
B. 30π cm²
C. 100π cm²
D. 25π cm²

ANSWER= D. 25π cm²

 

15. The perimeter of a square circumscribing a circle of radius a units is

A. 2 units
B. 4α units
C. 8α units
D. 16α units

ANSWER= C. 8α units

 

16. The perimeter of the sector with radius 10.5 cm and sector angle 60° is

A. 32 cm
B. 23 cm
C. 41 cm
D. 11 cm

ANSWER= A. 32 cm

 

17. In a circle of diameter 42 cm, if an arc subtends an angle of 60° at the centre, where π = 227 then length of arc is

A. 11 cm
B. 227 cm
C. 22 cm
D. 44 cm

ANSWER= C. 22 cm

 

18. The perimeter of a sector of radius 5.2 cm is 16.4 cm, the area of the sector is

A. 31.2 cm²
B. 15 cm²
C. 15.6 cm²
D. 16.6 cm²

ANSWER= C. 15.6 cm²

 

19. If the perimeter of a semicircular protractor is 72 cm where π = 227, then the diameter of protractor is

A. 14 cm
B. 33 cm
C. 28 cm
D. 42 cm

ANSWER= C. 28 cm

 

20. If the radius of a circle is doubled, its area becomes

A. 2 times
B. 4 times
C. 8 times
D. 16 times

ANSWER= B. 4 times

 

21. If the sum of the circumferences of two circles with radii R1 and R2 is equal to circumference of a circle of radius R, then

A. R1 + R2 = R
B. R1 + R2 > R
C. R1 + R2 < R
D. Can’t say;

ANSWER= A. R1 + R2 = R

 

22. The perimeter of a circular and square fields are equal. If the area of the square field is 484 m² then the diameter of the circular field is

A. 14 m
B. 21 m
C. 28 m
D. 7 m

ANSWER= C. 28 m

 

23. The radius of sphere is r cm. It is divided into . two equal parts. The whole surface area of two parts will be

A. 8πr² cm²
B. 6πr² cm²
C. 4πr² cm²
D. 3πr² cm²

ANSWER= B. 6πr² cm²

 

24. If the diameter of a semicircular protractor is 14 cm, then its perimeter is .

A. 27 cm
B. 36 cm
C. 18 cm
D. 9 cm

ANSWER= B. 36 cm

 

25. A race track is in the form of a circular ring whose outer and inner circumferences are 396 m and 352 m respectively. The width of the track is

A. 63 m
B. 56 m
C. 7 m
D. 3.5 m

ANSWER= C. 7 m

 

26. The area of the largest square that can be inscribed in a circle of radius 12 cm is

A. 24 cm²
B. 249 cm²
C. 288 cm²
D. 196√2 cm²

ANSWER= C. 288 cm²

 

27. The area of the largest triangle that can be inscribed in a semicircle of radius r is

A. r²
B. 2r²
C. r³
D. 2r³

ANSWER= A. r²

 

28. The area (in cm²) of the circle that can be inscribed in a square of side 8 cm is

A. 64 π
B. 16 π
C. 8 π
D. 32 π

ANSWER= B. 16 π

 

29. If the perimeter of a circle is equal to that of a square, then the ratio of their areas is

A. 22 : 7
B. 14 : 11
C. 7 : 22
D. 11 : 14

ANSWER= B. 14 : 11

 

30. The circumference of two concentric circles forming a ring are 88 cm and 66 cm. Taking π = 227, the width of the ring is

A. 14 cm
B. 7 cm
C. 72 cm
D. 21 cm

ANSWER= C. 72 cm

 

31. A steel wire when bent in the form of a square encloses an area of 121 cm². If the same wire is bent in the form of a circle, then the circumference of the circle is

A. 88 cm
B. 44 cm
C. 22 cm
D. 11 cm

ANSWER= B. 44 cm

 

32. The diameter of a circle whose area is equal to sum of the areas of the two circles of radii 40 cm and 9 cm is

A. 41 cm
B. 49 cm
C. 82 cm
D. 62 cm

ANSWER= C. 82 cm

 

33. If the area of a circle is numerically equal to twice its circumference, then the diameter of the circle is

A. 4 units
B. n units
C. 8 units
D. 2 units

ANSWER= C. 8 units Explaination: C. πr² = 2πr × 2 ⇒ r = 4 ⇒ 2r = 8 units

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