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## Geometry and Mensuration: Level 2 Test 8

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*Geometry and Mensuration: Level 2 Test 8*. You scored %%SCORE%% out of %%TOTAL%%. You correct answer percentage: %%PERCENTAGE%% . Your performance has been rated as %%RATING%% Your answers are highlighted below.

Question 1 |

In a circle of radius 17 cm, two parallel chords are drawn on opposite sides of a diameter. The distance between the chords is 23 cm. If length of one chord is 16 cm, then the length of the other is

15 cm | |

23 cm | |

30 cm | |

34 cm |

Question 1 Explanation:

Let half the length of one chord = 16/2 = 8 cm.

Thus one part of the perpendicular distance of the chord is 15 cm (by Pythagoras theorem)

The other part is 23-15 = 8 cm

Thus half the length of the other chord = 15 cm (by Pythagoras theorem)

Thus the length of the other radius = 2X 15= 30 cm

Correct option is (c)

Question 2 |

If the area of a square inscribed in a circle is 15 cm

^{2}, then the area of the square inscribed in a semicircle of the same circle, in cm^{2}, is5 | |

6 | |

7.5 | |

√50 |

Question 3 |

Diameter of a cylindrical jar is increased by 25%, By what percent must the height be decreased so that there is no change in its volume?

18% | |

25% | |

32% | |

36% |

Question 3 Explanation:

The diameter is increased by 25% and thus the radius has increased by 25%

i.e. 5/4 of the previous length.

The volume is a function of square of the radius and height.

Thus the height should decrease by 16/25 = 36%.

i.e. 5/4 of the previous length.

The volume is a function of square of the radius and height.

Thus the height should decrease by 16/25 = 36%.

Question 4 |

The sides of a triangle are 5, 12 and 13 units. A rectangle is constructed, which is equal in area to the triangle, has a width of 10 units. Then, the perimeter of the rectangle is:

30 units | |

36 units | |

13 units | |

None of these |

Question 4 Explanation:

Sides of the triangle = 5,12,13

We can say that it is right angled triangle with length 12 , hypotenuse 13 and height 5

So the area of the triangle = ½ x 12 x 5 = 30

Acc. to question

A rectangle is constructed, which is equal in area to the triangle, has a width of 10 units.

Therefore

Length x 10 = 30

Length = 3

Therefore the perimeter of the triangle = 2(l+b) = 2(13 ) = 26 units

We can say that it is right angled triangle with length 12 , hypotenuse 13 and height 5

So the area of the triangle = ½ x 12 x 5 = 30

Acc. to question

A rectangle is constructed, which is equal in area to the triangle, has a width of 10 units.

Therefore

Length x 10 = 30

Length = 3

Therefore the perimeter of the triangle = 2(l+b) = 2(13 ) = 26 units

Question 5 |

For a triangle, base is 6√3cm and two base angles are 30

^{o}and 60^{o}. Then height of the triangle is$ \displaystyle 3\sqrt{3}$ | |

$ \displaystyle 4.5$ | |

$ \displaystyle 4\sqrt{3}$ | |

$ \displaystyle 2\sqrt{3}$ |

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