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SSC - Mensuration Test-4
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SSC - Mensuration Test-4
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  • Question 1/10
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    The area of the square field is 196 sq.m. Its each side is:

    Solutions

    Let the side of each square is P. 

    Area of the square = P2 

    P2 = 196 

    P = 14 

    Hence, the side of a square is 14 m.

     

  • Question 2/10
    1 / -0

    If the length of a rectangle is increased by 50% then by how much percent its width should be reduced to keep the area same?

    Solutions

    Percentage increase in length =50%  

    Then the required percentage reduction in width = 50 / 100 + 50 × 100  = 33 1/3 %

     

  • Question 3/10
    1 / -0

    The circumference of a circle is equal to the perimeter of an equilateral triangle. If the radius of the circle is 10.5 cm what is the length of the side of the equilateral triangle?

    Solutions

    let side of the equilateral triangle be a cm 

    Given: The circumference of a circle is equal to the perimeter of an equilateral triangle 

    ∴Perimeter of the triangle = 2 π r 

    ⇒3a = 2 × 22/7 × 10.5 

    ⇒ a = 22 cm

     

  • Question 4/10
    1 / -0

    If the radius of a sphere is thrice than that of a hemisphere, then what will be the ratio of their respective volumes?

    Solutions

    Let the radius of hemisphere =a 

    Then radius of sphere =3a 

    Volume of sphere = 4 /3  π27 a3

    Volume of hemisphere = 2/3 πa3

    So required ratio= 4× 27:2=54:1

     

  • Question 5/10
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    An equilateral triangle of side 6 cm has its corners cut off to form a regular hexagon. Area (in cm2) of this regular hexagon will be

    Solutions

     

  • Question 6/10
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    The radius of a circle is a side of a square. The ratio of the areas of the circle and the square is

    Solutions

     

  • Question 7/10
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    The rain water from a roof 22 m × 20 m drains into a cylindrical vessel having a diameter of 2 m and height 3.5 m. If the vessel is just full, then the rainfall in cm is:

    Solutions

     

  • Question 8/10
    1 / -0

    The base of a right prism is a right-angled triangle whose sides are 5 cm, 12 cm and 13 cm. if the total surface area of the prism is 360 cm2, then its height (in cm) is:

    Solutions

    Total surface area = perimeter of base × height + 2(Area of base) 

    ⇒ 360 = 30×h +  2((1/2)×5×12) 

    ⇒ 360 = 30h + 60

    ⇒ 360 - 60 = 30h

    ⇒ h = 10 cm 

    Hence option A is correct.

     

  • Question 9/10
    1 / -0

    The base of right prism is a triangle whose perimeter is 28 cm and the inradius of the triangle is 4 cm. If the volume of the prism is 366 cc, then its height is

    Solutions

    Volume of prism = Area of base × height 

    Area of base= inradius*semi pereimeter

                       =(4*28)/2

     

  • Question 10/10
    1 / -0

    If the length of each side of an equilateral triangle is increased by 2 unit, the area is found to be increased by (3+√3) square unit. The length of each side of the triangle is

    Solutions

     

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