- This is an assessment test.
- These tests focus on geometry and mensuration and are meant to indicate your preparation level for the subject.
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## Geometry and Mensuration: Test 5

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Question 1 |

The length of a rectangular floor is twice its breadth. If Rs.256 is required to paint the floor at the rate of Rs.2 per square meters, then what would be the length of floor?

16 metres
| |

8 metres | |

12 metres | |

32 metres |

Question 1 Explanation:

Let the length be 2x units and breadth = x units.

Area = 256/2 =128 = 2x

So breadth x= 8 and length = 16 units .

Correct option is (a)

Area = 256/2 =128 = 2x

^{2}So breadth x= 8 and length = 16 units .

Correct option is (a)

Question 2 |

The circumference of two circles Is 132 metres and 176 metres respectively. What Is the difference between the area of the larger circle and the smaller circle?

1048 sq. metres | |

1076 eq. metres | |

1078 sq. metres | |

1090 sq. metres |

Question 2 Explanation:

$ \displaystyle \begin{array}{l}Let\text{ }the\text{ }radius\text{ }of\text{ }larger\text{ }circle\text{ }be\text{ }R\text{ }m\\and\text{ }smaller\text{ }circle\text{ }be\text{ }r\text{ }m.~\\2\pi r=132\\=>r=21\\and\,2\pi r=176\\=>r=28m\\Difference\text{ }between\text{ }the\text{ }areas\\\frac{22}{7}\times ({{28}^{2}}-{{21}^{2}})\\=49\times 22=1078{{m}^{2}}~~~~~~~~~~~\end{array}$

Question 3 |

What would be the cost of building a fence around a circular field with area equal to 32378.5 sq. metres, if the price per metre for building the fence was Rs.154?

Rs.84, 683 | |

Rs.86, 495 | |

Rs.79, 326 | |

Rs.98, 252 |

Question 3 Explanation:

$ \begin{array}{l}\pi {{r}^{2}}=32378.5\\=>r=101.52\\2\pi r=2\times \frac{22}{7}\times 101.5\\=637.74\\Total\,\,\cos t\,=637.74\times 154=98212\end{array}$

Question 4 |

The perimeter of a square is equal to twice the perimeter of a rectangle of length 8 cm, and breadth 7 cm. What is the perimeter of a semicircle whose diameter is equal to the side of the square? (Rounded off to the two decimal places)

38.57 cms. | |

23.57 cms. | |

42.46 cms. | |

47.47 cms. |

Question 4 Explanation:

Perimeter of the rectangle = 2(8+7) = 30 cm.

Perimeter of square = 30 X 2 = 60 cm.

Side of the square = 60/4 = 15 cm.

Radius of semicircle = 7.5 cm.

Perimeter of semicircle

$ \pi r+2r=\frac{22}{7}\times 7.5+15=23.57+15=38.57cm$

Perimeter of square = 30 X 2 = 60 cm.

Side of the square = 60/4 = 15 cm.

Radius of semicircle = 7.5 cm.

Perimeter of semicircle

$ \pi r+2r=\frac{22}{7}\times 7.5+15=23.57+15=38.57cm$

Question 5 |

The perimeter of a square is double the perimeter of a rectangle. The area of the rectangle is 240 sq. cm. What is the area of the square?

100 sq. cm. | |

36 sq. cm. | |

81 sq. cm. | |

Cannot be determined |

Question 5 Explanation:

Nothing is mentioned about length or breadth of the rectangle.

Thus the area of square cannot be determined. Correct option is (d)

Thus the area of square cannot be determined. Correct option is (d)

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