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) πr2
➩ (1 / 4) * π * (22 / π)2
➩ (1 / 4) * π * (22 / π) * (22 / π)
➩ 121 / π cm2
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) * πr2
= (90 / 360) * (22 / 7) * (5)2
= (1 / 4) * (22 / 7) * (5) * (5)
= 39.28 m2
3. Which of the following options is correct if the sum of the circumferences of two smaller circles with radii r1 and r2 is equal to 4 times the circumference of a bigger circle of radius r?
a) r1 / r2 = 2r
b) r1 + r2 = 4r
c) r1 * r2 = r / 4
d) r1 + r2 < 3r / 2
View Answer
Explanation: According to the question,
Circumference of r1 + circumference of r2 = 4 * circumference of r
2πr1 + 2πr2 = 4 * 2πr
On cancelling 2π on both the sides gives,
r1 + r2 = 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 = πr2
➩ Area = π (6)2
➩ Area = 36π cm2
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,
➩ πr2 = 2(2πr)
➩ πr2 = 4πr
➩ r = 4 cm
Circumference = 2πr
➩ 2 * (22 / 7) * 4
➩ 25.14 cm2
6. What is the diameter of the circle if its area is 154 m2?
a) 7
b) 49
c) 14
d) 21
View Answer
Explanation: Given,
Area of circle = 154 m2
➩ πr2 = 154
➩ r2 = 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) * πr2
➩ (1 / 2) * (22 / 7) * (5)2
➩ (1 / 2) * (22 / 7) * (25)
➩ 39.28 cm2
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 = πr2
➩ (22 / 7) * 49 * 49
➩ 7546 m2
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) πr2
➩ (1 / 4) * π * (11 / π) * (11 / π)
➩ 121 / 4π
➩ 9.63 cm2
10. The area of a circle is 200 cm2. What will be its diameter?
a) 16 cm
b) 14 cm
c) 12 cm
d) 15 cm
View Answer
Explanation: Given,
➩ πr2 = 200
➩ r2 = 200 * 7 / 22
➩ r is almost equal to 8 cm.
➩ Diameter = 2r
= 2 * 8
= 16 cm
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