Area - Quantitative Aptitude
Q11. Area of four walls of a room is 66 m2 and its length and bredth are 7.5 m and 3.5 m respectively. The height of the room is
(a) 3 m
(b) 5 m
(c) 6 m
(d) 7 m
Answer: (a) 3 m
l = 7.5 m b = 3.5 m
Now 2 (l + b) X h = 66
⇒ 2 (7.5 + 3.5) X h = 66
⇒ 2 X 11 X h = 66
⇒ h = 3 m
Q12. A wheel makes 1000 revolutions in covering a distance of 88 km. The diameter of the wheel is
(a) 20 m
(b) 22 m
(c) 25 m
(d) 28 m
Answer: (d) 28 m
| Distance covered in 1 revolution = | 88 m | = | 88 X 1000 m | = 88 m |
| 1000 | 1000 |
∴ Circumference = 88 m
⇒ 2πr = 88
| ⇒ r = | 88 | = | 44 | = 14 m |
| 2π | 22/7 |
Diameter = 2 X 14m = 28m
Q13. The length of minute hand of a wall clock is 7 cm. The area swept by it in 15 minutes is
(a) 23.5 cm2
(b) 32.5 cm2
(c) 38.5 cm2
(d) 47.5 cm2
Answer: (c) 38.5 cm2
Angle swept in 15 minutes = 900
| Area swept = | πr2Θ | = | 22/7 X 7 X 7 X 900 | = | 22 X 7 | = | 77 | = 38.5 cm2 |
| 3600 | 3600 | 4 | 2 |
Q14. The radius of a wheel is 0.21 m. How many times does it revolve during a journey of 0.792 km ?
(a) 550
(b) 600
(c) 650
(d) 675
Answer: (b) 600
radius = 0.21 m
Circumference = 2πr = 2 X 22/7 X 0.21 m = 44 X 0.03 m = 1.32 m
| No of revolution = | 0.792 X 1000 m | = | 79200 | = 600 |
| 1.32 m | 132 |
Q15. In a circle of radius 14 cm, an arc subtends an angle of 60°at the center. The length of the arc is
(a) 12 1/3 cm
(b) 14 2/3 cm
(c) 15 1/3 cm
(d) 19 1/3 cm
Answer: (b) 14 2/3 cm
| Arc length = | 2πrΘ | = | 2 X 22/7 X 14 X 60° | = | 2 X 22 X 2 | = | 44 | = 14 | 2 | cm |
| 360° | 360° | 6 | 3 | 3 |
Q16. The radius of the wheel of a vehicle is 70 cm. The wheel makes 100 revolutions in 50 seconds. The speed of the vehicle is
(a) 8.8 m/sec
(b) 9.2 m/sec
(c) 10.5 m/sec
(d) 11.2 m/sec
Answer: (a) 8.8 m/sec
Circumference of the wheel = 2πr = 2 X 22/7 X 70 cm = 440 cm
| Distance covered in 100 revolution = 440 X 100 cm = | 440 X 100 | m = 440 m |
| 100 |
| Speed = | 440 m | = 8.8 m/sec |
| 50 sec |
Q17. The area of a rhombus is 72 cm2. One of its diagonals is thrice the other. The length of the shorter diagonal is
(a) 2√3 cm
(b) 3√3 cm
(c) 4√3 cm
(d) 5√3 cm
Answer: (c) 4√3 cm
Let the length of the shorter diagonal be x cm
∴ Longer diagonal = 3x cm
A/Q ½ X x X 3x = 72
⇒ 3x2 = 144
⇒ x2 = 48
⇒ x = 4√3 cm
Q18. If a square and a rhombus stand on the same base, then the ratio of the areas of the square and rhombus is
(a) 1
(b) 2
(c) 4
(d) 5
Answer: (a) 1
Let ABCD be the square and ABEF be the rhombus
Δ ADF = Δ BCE
⇒ Δ ADF + trap ABCF = Δ BCE + trap ABCF
⇒ area of ABCD = area of ABEF
| ⇒ | area of ABCD | = 1 |
| area of ABEF |
Q19. A triangle has sides of length 3 cm, 4 cm and 5 cm. What is the area of the circle inscribed in the triangle ?
(a) π cm2
(b) r cm2
(c) 1 cm2
(d) ½ cm2
Answer: (a) π cm2
a = 3 cm b = 4 cm c = 5 cm
| s = | 3 + 4 + 5 | = 6 cm |
| 2 |
| Δ = | |
| √ s(s-a) (s-b) (s-c) |
| = | |
| √ 6 X 3 X 2 X 1 |
= 6 cm2
| Radius of incircle= | Δ | = | 6 | = 1 cm |
| s | 6 |
∴ Area of the incircle = πr2 = π . 12 = π cm2
Q20. What is the diameter of a wheel that makes 113 revolutions to go 2 km 26 decameters ?
(a) 60/11 m
(b) 67/11 m
(c) 70/11 m
(d) 75/11 m
Answer: (c) 70/11 m
Distance = 2 km 26 decameters = 2 X 1000 m + 26 X 10m = 2260 m
Distance covered in 1 revolution = 2260/113 m = 20 m
Circumference = 20 m
⇒ 2πr = 20 m
⇒ 2 X 22/7 X r = 20
| ⇒ r = | 20 X 7 | = | 35 |
| 2 X 22 | 11 |
| ∴ Diameter = 2 X r = 2 X | 35 | = | 70 | m |
| 11 | 11 |
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