MathematicsFrom a solid cylinder whose height is 24 cm  and diameter 20 cm  , a conical cavity of same height and same diameter is hollowed out. Find the total surface area of the remaining solid.

From a solid cylinder whose height is 24 cm  and diameter 20 cm  , a conical cavity of same height and same diameter is hollowed out. Find the total surface area of the remaining solid.


  1. A
    2600 cm2
  2. B
    2640 cm2
  3. C
    2145 cm2
  4. D
    2500 cm2 

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    Solution:

    Given that from a solid cylinder having diameter 20 cm and height 24 cm, a conical cavity of same diameter and height is hollowed out.
    The curved surface area of a cylinder of radius, r and height, h is given by 2πrh  .
    The curved surface area of a cone of radius, r, slant height, l and height, h is given by πrl   where l= r 2 + h 2  .
    Radius of conical cavity is r= 20 2 =10cm  .
    The height of cone is 24 cm.
    Therefore,
    l= 10 2 + 24 2 l= 100+576 l= 676 l=26cm  
    The slant height of the cone is 26 cm.
    The curved surface area of cylinder = 2πrh  .
    ⇒ CSA of cylinder =2×π×10×24   ⇒ CSA of cylinder =480π   c m 2   The curved surface area of cone = πrl  .
    ⇒ CSA of cone =π×10×26   ⇒ CSA of cone =260π   c m 2  
    The area of upper circular base of cylinder by = π r 2  .
    ⇒ Area =π×10×10   ⇒Area =100π   The total surface area of remaining solid = CSA of cylinder + CSA of cone + Area of circular base.
    TSA=480π+260π+100π  
    ⇒ TSA =840π  
    ⇒ TSA =840× 22 7  
    ⇒ TSA = 2640 c m 2  
    Hence, the total surface area of remaining solid is 2640 cm 2  .
    Therefore, the correct answer is option (2).
     
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