Ratio of Curved Surfaces of Sphere, Cylinder and Cone

A sphere, a cylinder and a cone are of the same radius and same height. The ratio of their curved surfaces area is

  1. 4: √5 :4
  2. 2: 2: √5
  3. 4: 4: 5
  4. 4: 4: √5
Manish Listener Asked on 15th June 2015 in Maths.
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  • 1 Answer(s)

    Answer: 4 : 4 : √5

    Solution:

    It is provided in question that radius & height of sphere, cylinder and cone are same.
    i.e.  h= h2 = h = h    &    r1 = r2 = r3 =  r

    As we know that,
    Surface Area of Sphere : 4 π r12
    Curved Surface Area of cylinder: 2 π r2 h2
    Curved Surface Area of cone: π r3 l    –>  where l is slant height, l = sqrt(r32 + h3 2 )

    ratio of curved surfaces is:
    -> 4 π r12   :  2 π r2 h2  :  π r3 sqrt(r32 + h3 2 )

    as per condition given in the question we can show that,
    Height of sphere, h1 = 2 x radius = 2 r , i.e. h = 2r

    so, ratios can be simplified as

    -> 4 π r2   :  2 π r (2r)  :  π r sqrt(r2 + (2r) 2 )
    -> 4 r  :  2 (2r)  :  sqrt(5r2 )
    -> 4 r  :  4  r  :  r sqrt(5)
    -> 4 : 4 : sqrt(5)    # final answer

    Also remember:

    Volume of Sphere: (4/3) π r3
    Volume of cylinder: π r2 h
    Volume of cone: (1/3) π r2 h

    Pushpendra Pal Dean Answered on 31st October 2014.
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