This set of Aptitude Questions and Answers (MCQs) focuses on “Circles”.

1. What will be the area (in sq. cm) of a quadrant of a circle which has a circumference of 44cm?

a) 110 / π

b) 22 / π

c) 121 / π

d) 11 / π

View Answer

Explanation: Given,

Circumference = 44 cm

➩ 2πr = 44

➩ r = 44 / 2π = 22 / π

Area of quadrant = (1 / 4) πr

^{2}

➩ (1 / 4) * π * (22 / π)

^{2}

➩ (1 / 4) * π * (22 / π) * (22 / π)

➩ 121 / π cm

^{2}

2. A horse is tied to a peg at one corner of a square shaped grass field of side 10 m by means of a 5 m long rope. What will be the area (in sq. m) of that part of the field in which the horse can graze?

a) 39.28

b) 41.46

c) 35.69

d) 42.57

View Answer

Explanation: Given,

r = 5 m, angle in degree = 90.

➩ Area of the sector = (angle in degree / 360) * πr

^{2}

= (90 / 360) * (22 / 7) * (5)

^{2}

= (1 / 4) * (22 / 7) * (5) * (5)

= 39.28 m

^{2}

3. Which of the following options is correct if the sum of the circumferences of two smaller circles with radii r_{1} and r_{2} is equal to 4 times the circumference of a bigger circle of radius r?

a) r_{1} / r_{2} = 2r

b) r_{1} + r_{2} = 4r

c) r_{1} * r_{2} = r / 4

d) r_{1} + r_{2} < 3r / 2

View Answer

Explanation: According to the question,

Circumference of r

_{1}+ circumference of r

_{2}= 4 * circumference of r

2πr

_{1}+ 2πr

_{2}= 4 * 2πr

On cancelling 2π on both the sides gives,

r

_{1}+ r

_{2}= 4r

4. What will be the area (in sq. cm) of the circle that can be inscribed in a square of side 12 cm?

a) 36π

b) 216π

c) 64π

d) 60π

View Answer

Explanation: According to the question,

The diameter of circle would be equal to the side of the square.

➩ d = 12 cm

➩ r = 12 / 2 = 6 cm

➩ Area = πr

^{2}

➩ Area = π (6)

^{2}

➩ Area = 36π cm

^{2}

5. What will be the circumference of the circle if its area is numerically equal to twice its circumference?

a) 35.38

b) 50.28

c) 25.14

d) 42.72

View Answer

Explanation: Given,

➩ πr

^{2}= 2(2πr)

➩ πr

^{2}= 4πr

➩ r = 4 cm

Circumference = 2πr

➩ 2 * (22 / 7) * 4

➩ 25.14 cm

^{2}

6. What is the diameter of the circle if its area is 154 m^{2}?

a) 7

b) 49

c) 14

d) 21

View Answer

Explanation: Given,

Area of circle = 154 m

^{2}

➩ πr

^{2}= 154

➩ r

^{2}= 154 * 7 / 22

➩ r = 7 m

➩ diameter = 2r = 2 * 7 = 14 m

7. What will be the area (in sq. cm) of a protractor if its diameter is 10 cm?

a) 39.28

b) 43.96

c) 35.24

d) 32.68

View Answer

Explanation: Diameter = 10 cm, thus, radius = 5cm.

As protector is semicircle in shape,

Area of protractor = (1 / 2) * πr

^{2}

➩ (1 / 2) * (22 / 7) * (5)

^{2}

➩ (1 / 2) * (22 / 7) * (25)

➩ 39.28 cm

^{2}

8. What will be the area (in sq. m) of the circle formed by the same steel wire which forms a square of perimeter 308 m?

a) 6210

b) 8532

c) 7546

d) 9478

View Answer

Explanation: According to the question,

Perimeter of square = circumference of the circle.

➩ 2πr = 308

➩ 2 * (22 / 7) * r = 308

➩ r = 308 * 7 / (2 * 22)

➩ r = 49m.

Area of circle = πr

^{2}

➩ (22 / 7) * 49 * 49

➩ 7546 m

^{2}

9. What will be the area (in sq. cm) of a quadrant of the circle whose border length is 22 cm?

a) 11.62

b) 9.63

c) 7.58

d) 13.19

View Answer

Explanation: Given,

➩ 2πr = 22

➩ r = 11 / π

Area of the quadrant = (1 / 4) πr

^{2}

➩ (1 / 4) * π * (11 / π) * (11 / π)

➩ 121 / 4π

➩ 9.63 cm

^{2}

10. The area of a circle is 200 cm^{2}. What will be its diameter?

a) 16 cm

b) 14 cm

c) 12 cm

d) 15 cm

View Answer

Explanation: Given,

➩ πr

^{2}= 200

➩ r

^{2}= 200 * 7 / 22

➩ r is almost equal to 8 cm.

➩ Diameter = 2r

= 2 * 8

= 16 cm

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