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## Geometry and Mensuration: Level 1 Test 10

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Question 1 |

The length and breadth of a playground are 36 m and 21 m respectively. Poles are required to be fixed all along the boundary at a distance 3 m apart. The number of poles required will be

39 | |

38 | |

37 | |

40 |

Question 1 Explanation:

$\displaystyle \begin{array}{l}The\text{ }total\text{ }number\text{ }of\text{ }the\text{ }poles\text{ }=\\\frac{36}{3}+1+\frac{21}{3}+1+\frac{21}{3}-1+\frac{36}{3}-1\\=\,12+1+7+1+7+12-1-1=38\end{array}$

Question 2 |

. The perimeters of a square and a regular hexagon are equal. The ratio of the area of the hexagon to the area of the square is

2√3: 3 | |

√3: 1 | |

3√3: 2 | |

√2 : 3 |

Question 2 Explanation:

Let the perimeter be 24 cm.

Thus the area of the square = (24/4)

The side of the hexagon = 24/6 cm=4 cm.

There are 6 equilateral triangles in the hexagon.

Each equilateral triangle = (√3/4)x4

Thus the total area of hexagon = 24√3 cm

The required ratio =24√3 : 36 = 2√3 : 3

Thus the area of the square = (24/4)

^{2 }=36 cm^{2}The side of the hexagon = 24/6 cm=4 cm.

There are 6 equilateral triangles in the hexagon.

Each equilateral triangle = (√3/4)x4

^{2 }=4√3 cm^{2}Thus the total area of hexagon = 24√3 cm

^{2}=24√3The required ratio =24√3 : 36 = 2√3 : 3

Question 3 |

A rectangular piece of cardboard 18 cm x 24 cm is made into an open box by cutting a square of 5 cm side from each corner and build up the side. Find the volume of the box.

432 cu cm | |

560 cu cm | |

216 cu cm | |

None of these |

Question 3 Explanation:

The volume of the box is

(18-2x5)(24-2x5)(5) = 560 cu m.

Correct option is (b)

(18-2x5)(24-2x5)(5) = 560 cu m.

Correct option is (b)

Question 4 |

The locus of a point equidistant from the two fixed points is

Any straight line bisecting the segment joining the fixed points | |

Any straight line perpendicular to the segment joining the fixed points | |

The straight line which is perpendicular bisector of the segments joining the fixed points | |

Any straight line perpendicular to the line joining the fixed points |

Question 5 |

Any cyclic parallelogram having unequal adjacent sides is necessarily a

Square | |

Rectangle | |

Rhombus | |

Trapezium |

Question 5 Explanation:

A cyclic quadrilateral has the sum of diagonally opposite angles = 180

The diagonally opposite angles in a parallelogram are equal.

Thus the angles of the cyclic parallelogram = 90

^{o }The diagonally opposite angles in a parallelogram are equal.

Thus the angles of the cyclic parallelogram = 90

^{o }The cyclic parallelogram is necessarily a rectangle.
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