# Area - Quantitative Aptitude

Q11. Area of four walls of a room is 66 m^{2} 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 cm^{2}

(b) 32.5 cm^{2}

(c) 38.5 cm^{2}

(d) 47.5 cm^{2}

**Answer:** (c) 38.5 cm^{2}

Angle swept in 15 minutes = 90^{0}

Area swept = | πr^{2}Θ |
= | ^{22}/_{7} X 7 X 7 X 90^{0} |
= | 22 X 7 | = | 77 | = 38.5 cm^{2} |

360^{0} |
360^{0} |
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 cm^{2}. 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

⇒ 3x^{2} = 144

⇒ x^{2} = 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 cm^{2}

(b) r cm^{2}

(c) 1 cm^{2}

(d) ½ cm^{2}

**Answer:** (a) π cm^{2}

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 cm^{2}

Radius of incircle= | Δ | = | 6 | = 1 cm |

s | 6 |

∴ Area of the incircle = πr^{2} = π . 1^{2} = π cm^{2}

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 |