# Volume and Surface Area

## Volume and Surface Area

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Question 1 |

In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

75 cu. m | |

750 cu. m | |

7500 cu. m | |

75000 cu. m |

Question 1 Explanation:

1 hectare = 10,000 m^2
So, Area = (1.5 x 10000) m^2 = 15000 m^2.
Depth = 5/100m =1/20m.
Volume = (Area x Depth) =15000 x(1/120)m^3= 750 m^3.

Question 2 |

A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

1200 | |

900 | |

720 | |

1800 |

Question 2 Explanation:

2(15 + 12) x h = 2(15 x 12)
h = 180/27 m =20/3 m.
Volume =15 x 12 x(20/3)m^3 = 1200 m^3.

Question 3 |

6 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:
A.
B.
C.
D.
Answer: Option A
Explanation:
Let the length of the wire be h.
Radius = 1 mm = 1 cm. Then,
2 20
22 x 1 x 1 x h = 66.
7 20 20
h = 66 x 20 x 20 x 7 = 8400 cm = 84 m.
22

84 | |

90 | |

168 | |

336 |

Question 3 Explanation:

Let the length of the wire be h.
Radius =1/2mm =1/20cm. Then,
==>(22/7)x(1/20)x(1/20)x h = 66.
h =(66 x 20 x 20 x 7)/22= 8400 cm = 84 m.

Question 4 |

A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:

12 kg | |

60 kg | |

72 kg | |

96 kg |

Question 4 Explanation:

Volume of water displaced= (3 x 2 x 0.01) m^3 = 0.06 m^3.
Mass of man = Volume of water displaced x Density of water
= (0.06 x 1000) kg = 60 kg.

Question 5 |

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:

20 cm | |

25 cm | |

35 cm | |

50 cm |

Question 5 Explanation:

Total volume of water displaced = (4 x 50) m3 = 200 m3.
Rise in water level = 200/(40 x 20)m* 0.25 m = 25 cm.

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