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## Geometry and Mensuration: Level 1 Test 9

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Question 1 |

The number of bricks, each measuring 25 cm x 12.5 cm x 7.5 cm, required to construct a wall 6 m long, 5 m high and 0.5 m thick, while the mortar occupies 5% of the volume of the wall, is

5740 | |

6080 | |

3040 | |

8120 |

Question 1 Explanation:

$ \displaystyle Total\text{ }number\text{ }of\text{ }bricks\text{ }required\text{ }=\frac{600\times 500\times 50\times 0.95}{25\times 12.5\times 7.5}=6080$

Question 2 |

A and B travel around a circular path at uniform speeds in opposite directions, starting from diametrically opposite points, at the same time. They meet each other first after B has travelled 100 metres and meet again 60 metres before A completed one round. The circumference of the park is

240 m | |

300 m | |

320 m | |

480 m |

Question 2 Explanation:

Let A travel x m in the first meeting and thus the ratio of speeds of A and B is x/100.

Total circumference = 2(x+100) as they were diametrically opposite.

In the 2

B has travelled = 100+x+60 = 160+x,

Ratio of speed A:B = 2x+140/160+x

Equating the two ratios we will get,

x= 140.

Thus the circumference = 2X140+200 = 480 m

Total circumference = 2(x+100) as they were diametrically opposite.

In the 2

^{nd}meeting A has travelled 2x+200-60 = 2x+140.B has travelled = 100+x+60 = 160+x,

Ratio of speed A:B = 2x+140/160+x

Equating the two ratios we will get,

x= 140.

Thus the circumference = 2X140+200 = 480 m

Question 3 |

If the radius of circle is increased by 50%, then the area of the circle is increased by

125% | |

100% | |

75% | |

50% |

Question 3 Explanation:

Area is directly proportional to r

=> Area is directly proportional to (1.5 r

=> Area is directly proportional to 2.25r

The area has increased by (2.25 -1)x100 = 125%

^{2}=> Area is directly proportional to (1.5 r

^{2})=> Area is directly proportional to 2.25r

The area has increased by (2.25 -1)x100 = 125%

Question 4 |

Four sheets 50 cm x 5 cm are arranged without overlapping to form a square having side 55 cm. What is the area of inner square so formed?

2500 cm ^{2} | |

2025 cm ^{2} | |

1600 cm ^{2} | |

None of these |

Question 4 Explanation:

The side of the inner square = 55 â€“ 2 x 5 = 45 cm = 55 -2X5 = 45 cm.

The area of the inner square = 45

The area of the inner square = 45

^{2}=2025 cm^{2}Question 5 |

A photo measures 0.9 x cm by 0.94 x cm. It is to be enlarged so that the larger dimension will be 6 cm. The length of the enlarged shorter dimension will be

5.74x cm | |

5.4x cm | |

5.64x cm | |

7.09x cm |

Question 5 Explanation:

$latex \displaystyle The\text{ }required\text{ }length=\frac{0.9\times 6}{0.94}=5.74$

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