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## Geometry and Mensuration: Level 2 Test 9

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Question 1 |

Suface area of a cuboid is 22 cm

^{2}and the sum of the lengths of all its edges is 24 cm. Length of each diagonal of the cuboid (in cm) is145 | |

200 | |

122 | |

none |

Question 1 Explanation:

$ \displaystyle \begin{array}{l}Let\text{ }the\text{ }length\text{ },\text{ }width\text{ }and\text{ }height\text{ }be\text{ }l\text{ },\text{ }w\text{ }and\text{ }h\text{ }units\text{ }respectively\\l+b+w=\frac{24}{4}=6\\lb+bw+lw=\frac{22}{2}=11\\Now\,\,{{l}^{2}}+{{b}^{2}}+{{w}^{2}}+2lb+2bw+2lw={{(l+b+w)}^{2}}\\{{l}^{2}}+{{b}^{2}}+{{w}^{2}}+22=36\\{{l}^{2}}+{{b}^{2}}+{{w}^{2}}=14\\\sqrt{{{l}^{2}}+{{b}^{2}}+{{w}^{2}}}=\sqrt{14}\end{array}$

Question 2 |

A slab of ice 8 inches in length, 11 inches in breadth, and 2 inches thick was melted and re-solidified in the form of a rod of 8 inches diameter. The length of such a rod, in inches, in nearest to:

3 | |

3·5 | |

4 | |

4·5 |

Question 2 Explanation:

The volume of the ice slab =8X11X2

The volume of the rod (assuming length = h) =Πx42h = 8 x 11 x 2

h = 3.5

Correct option is (b)

The volume of the rod (assuming length = h) =Πx42h = 8 x 11 x 2

h = 3.5

Correct option is (b)

Question 3 |

Four friends start from four towns, which are at the four comers of an imaginary rectangle. They meet at a point which falls inside the rectangle, after travelling the distances of 40 m, 50 m and 60 m. The maximum distance that the fourth could have travelled is approximately:

67 m | |

52 m | |

22.5 m | |

Cannot be determined |

Question 3 Explanation:

Now we know that if we assume the length required =p resp,

then 50 x 40 = 60 x p

=> p = 50 x 40/60

=> p = 66.67

The correct option is (a)

then 50 x 40 = 60 x p

=> p = 50 x 40/60

=> p = 66.67

The correct option is (a)

Question 4 |

The length of a ladder is exactly equal to the height of the wall it is leaning against. H lower end of the ladder kept on a stool of height 3 m and the stool is kept 9 m away from the wall, the upper end of the ladder coincides with the top of the wall. Then, the height of the wall is:

12 m | |

15 m | |

18 m | |

11 m |

Question 5 |

An equilateral triangle and a regular hexagon have equal perimeters. The ratio of the area of the triangle and that of the hexagon is

1: 1 | |

2: 3 | |

3: 2 | |

3: 4 |

Question 5 Explanation:

Let the individual sides of the hexagon be 1 cm

Thus the perimeter =6 and the side of the equilateral triangle is 2cm.

Thus the area of the equilateral triangle = √3 x 4 = √3 cm.

Thus the area of the hexagon= {(6 x √3)/4} x 1

Thus the ratio of the triangle to hexagon is 2:3.

Correct option is (b)

Thus the perimeter =6 and the side of the equilateral triangle is 2cm.

Thus the area of the equilateral triangle = √3 x 4 = √3 cm.

Thus the area of the hexagon= {(6 x √3)/4} x 1

^{2}= 3/2√3Thus the ratio of the triangle to hexagon is 2:3.

Correct option is (b)

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