A solid cylinder has a total surface area of 231 cm² Its curved surface area is 2/3 of the total surface area. Find.the volume of the cylinder.

  1. 332 cm²
  2.  269.5 cm²
  3.  314.2 cm²
  4.  32 cm²

 

Anurag Mishra Professor Asked on 26th January 2016 in Maths.
Add Comment
  • 1 Answer(s)

    Answer: (2) 269.5 cm^3

    Explanation:-
    Total surface area of a cylinder = 231 cm^2
    Then, 2 pai x r(r + h) – 231  ………………. (1) 

    Curved surface area = 2/3 of total surface area  (Given in the question)
    Then,  2 x pai x r x h = 2 x 231/3
     2 x pai x r x h = 154
    h = 154/2 x pai x r …………………. (2) 

    From equation (1) , 
    2 x pai x (r + 154/2 x pai x r) = 231
    2 x pai x r^2 + 154 = 231
    2 pai r^2 = 231 – 154
    2 pai r ^2 = 77
    r^2 = 77/2 pai
    r^2 = 77 x 7 x 2/2 x 22 x 7
    r^2 = 49/4
    Square root on both side, 
    r = 7/2

    From equation (2), 
    h = 154 x 7 x 2/2 x 22 x 7
    h = 7 cm 

    Thus, volume of the cylinder = pai x r^2 x h
     = 22 x 7 x 7 x 7 /7 x 2 x 2
     = 11 x 7 x 7/2
     = 539/2
     = 269.5

    Then, the volume of the cylinder is (2) 269.5 cm^3

    Hence, the correct answer is option (2) 269.5 cm^3.

     

    Anurag Mishra Professor Answered on 26th January 2016.
    Add Comment
  • Your Answer

    By posting your answer, you agree to the privacy policy and terms of service.