- This is an assessment test.
- These tests focus on geometry and mensuration and are meant to indicate your preparation level for the subject.
- Kindly take the tests in this series with a pre-defined schedule.

## Geometry and Mensuration: Test 30

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Question 1 |

A grassy field has the shape of an equilateral triangle of side 6m. A horse is tied to one of its vertices with a rope of length 4.2m. The percentage of the total area of the field which is available for grazing is best approximated by

50% | |

55% | |

59% | |

62% |

Question 1 Explanation:

Question 2 |

The areas of two circles are in the ratio 1: 2. If the two circles are bent in the form of squares, what is the ratio of their areas?

1: 2 | |

1: 3 | |

1: √2 | |

1: 4 |

Question 2 Explanation:

Area of two circles in 1:2 then their perimeter will be in 1:√2 Since the circle is bent to form a square,

so the perimeter of square = circumference of the circle

So perimeters of squares will also be in 1:√2

So area of squares is 1²:(√2)²=1: 2

Correct option is (a)

so the perimeter of square = circumference of the circle

So perimeters of squares will also be in 1:√2

So area of squares is 1²:(√2)²=1: 2

Correct option is (a)

Question 3 |

A wall is of the form of a trapezium with height 4m and parallel sides being 3m and 5m. What is the cost of painting the wall, if the rate of painting is Rs.25 per sq m?

Rs.240 | |

Rs.400 | |

Rs.480 | |

Rs.800 |

Question 3 Explanation:

$ \begin{array}{l}The\text{ }area\text{ }of\text{ }the\text{ }wall=\frac{1}{2}(3+5)4=16\,sq\,m\\The\text{ }total\text{ }cost\text{ }=\text{ }25\times 16=Rs.\text{ }400.\\Correct\text{ }option\text{ }is\text{ }\left( b \right)\end{array}$

Question 4 |

The area of a rectangle whose length is 5 units more than twice its width is 75 sq units. What is the width?

3 units | |

5 units | |

7 units | |

10 units |

Question 4 Explanation:

Let the width of the rectangle be x units and thus length = 2x+5.

Thus, (2x+5)x=75

=>x=5.

Correct option is (b).

Thus, (2x+5)x=75

=>x=5.

Correct option is (b).

Question 5 |

The diameter of a circle circumscribing a square is 15√2cm. What is the length of the side of the square?

15 cm | |

12 cm | |

10 cm | |

7.5 cm |

Question 5 Explanation:

The diameter of the circle = diagonal of the square. Let the side of the square is 'x' cm.

So x

=> 2x

=> x

=> x = 15 cm

Thus the side= 15 cm Correct option is (a)

So x

^{2}+ x^{2}= (15√2)^{2}= 450=> 2x

^{2}= 450=> x

^{2}= 225=> x = 15 cm

Thus the side= 15 cm Correct option is (a)

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