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## Geometry and Mensuration: Test 4

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Question 1 |

What is the area of a circle whose circumference is 1047.2 metres?

87301.67 sq. meters | |

85142.28 sq. metres | |

79943.82 sq. metres | |

78621.47 sq. metres |

Question 1 Explanation:

$ \begin{array}{l}2\pi r=1047.2\\r=1047.2\times \frac{7}{2\times 22}=\frac{500}{3}\\\pi {{r}^{2}}=\frac{\frac{22}{7}\times \frac{500}{3}\times 500}{3}=87301\end{array}$

Question 2 |

An order was placed for supply of carpet of breadth 3 metres, the length of carpet was 1.44 times of breadth. Subsequently the breadth and length were increased by 25 and 40 per cent respectively. At the rate of Rs.45 per square metre, what would be the Increase In the cost of the carpet?

Rs.1020.6 | |

Rs.398.8 | |

Rs.437.4 | |

Rs.583.2 |

Question 2 Explanation:

The original breadth and length of the carpet is 3m and 3 Ã— 1.44 m respectively.

Question 3 |

The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 7803 sq. metre, what is the breadth of the rectangular plot?Let the breadth is 'b' and the length is '3b'.Area = 3b Ã— b = 7803=>3b

^{2}= 7803=>b^{2}= 2601 => b = 51 m.Correct option is (a)51 metres | |

153 metres | |

104 metres | |

88 metres |

Question 3 Explanation:

Let the breadth is 'b' and the length is '3b'.

Area = 3b Ã— b = 7803

=>3b

=>b

Area = 3b Ã— b = 7803

=>3b

^{2}= 7803=>b

^{2}= 2601 => b = 51 m. Correct option is (a)Question 4 |

The cost of fencing a circular plot at the rate of Rs.15 per metre is Rs.3, 300. What will be the cost of flooring the plot at the rate of Rs.100 per square metre?

Rs.3, 85, 000 | |

Rs.2, 20, 000 | |

Rs.3, 50, 000 | |

Cannot be determined |

Question 4 Explanation:

$ \displaystyle \begin{array}{l}Circumference\text{ }of\text{ }circle\text{ }=\text{ }3300/15\text{ }=\text{ }220m\\\frac{44}{7}r=220\\r=35\\Area=\pi {{r}^{2}}\\\frac{22}{7}\times 35\times 35=3850\end{array}$

Hence the cost of flooring = 3850 Ã— 100 = Rs 385000.

Hence the cost of flooring = 3850 Ã— 100 = Rs 385000.

Question 5 |

If the area of a circle is 616 cm

^{2}, what is its Circumference?76 cm. | |

84 cm. | |

96 cm. | |

none |

Question 5 Explanation:

Let 'r' be the radius of the circle.

Area of circle

$ \displaystyle \begin{array}{l}\pi {{r}^{2}}=616\\r=\sqrt{196}=14\\2\pi r=88m\end{array}$

Area of circle

$ \displaystyle \begin{array}{l}\pi {{r}^{2}}=616\\r=\sqrt{196}=14\\2\pi r=88m\end{array}$

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