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## Geometry and Mensuration: Level 1 Test 1

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Question 1 |

The area of circle is seven times the numerical value of its circumference. What is the circumference of the circle?

616 units | |

132 units | |

88 units | |

Cannot be determined |

Question 1 Explanation:

Let the radius of the circle be r units.

$ \begin{array}{l}\pi {{r}^{2}}=7\times 2\pi r\\=>r=14\\=>2\pi r=\frac{2\times 22}{7}\times 14=88units\\Correct\,\,option\,\,is\,\,(c)\end{array}$

$ \begin{array}{l}\pi {{r}^{2}}=7\times 2\pi r\\=>r=14\\=>2\pi r=\frac{2\times 22}{7}\times 14=88units\\Correct\,\,option\,\,is\,\,(c)\end{array}$

Question 2 |

AD is the median of a triangle ABC and O is the centroid such that AO= 10 cm. The length of OD in cm is

4 | |

5 | |

6 | |

8 |

Question 3 |

What will be the cost of gardening 1 metre broad boundary around a rectangular plot having perimeter of 340 metres at the rate of Rs.10 per square metre?

Rs.3, 400/- | |

Rs.1, 700/- | |

Rs.3, 440/- | |

Cannot be determined |

Question 3 Explanation:

Let the length be l and breadth be b units.

Area of the boundary= lb+2(l+b)+4-lb

= 2(l+b) +4 =344

The total cost = 344 x 10 = Rs. 3440

Correct option is (c)

Area of the boundary= lb+2(l+b)+4-lb

= 2(l+b) +4 =344

The total cost = 344 x 10 = Rs. 3440

Correct option is (c)

Question 4 |

5 cm | |

10 cm | |

5√2cm | |

2.5 cm |

Question 4 Explanation:

$ \begin{array}{l}AB=\sqrt{2\times {{5}^{2}}}\\AB=5\sqrt{2}\\The\,\,correct\,\,option\,\,is\,\,c\end{array}$

Question 5 |

The ratio of the length and the breadth of a rectangular plot is 6:5 respectively. If the breadth of the plot is 34 metres less than the length, what is the perimeter of the rectangular plot?

374 metres | |

408 metres | |

814 metres | |

748 metres |

Question 5 Explanation:

$ \displaystyle \begin{array}{l}Let\text{ }the\text{ }plot\text{ }be\text{ }of\text{ }length\text{ }and\text{ }breadth\text{ }6x\text{ }and\text{ }5x\text{ }units\text{ }resp.\\6x-5x\text{ }=\text{ }34.\\Thus\text{ }the\text{ }perimeter\text{ }=\text{ }2x\text{ }\left( 5x+6x \right)\text{ }\times ~34\text{ }=\text{ }22\times 34\text{ }=748\text{ }cm.\end{array}$

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