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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

A | 15 cm |

B | 23 cm |

C | 30 cm |

D | 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}, isA | 5 |

B | 6 |

C | 7.5 |

D | âˆš50 |

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?

A | 18% |

B | 25% |

C | 32% |

D | 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:

A | 30 units |

B | 36 units |

C | 13 units |

D | 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 = Â½ 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)Â = 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 = Â½ 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)Â = 2(13 ) = 26 units

Question 5 |

For a triangle, base is 6âˆš3cm and two base angles are 30

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

B | $ \displaystyle 4.5$ |

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

D | $ \displaystyle 2\sqrt{3}$ |

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