MathematicsThe height of a right circular cylinder is 10.5 m  . Three times the sum of the areas of its two circular faces is twice the area of the curved surface. What is the volume of the cylinder?

The height of a right circular cylinder is 10.5 m  . Three times the sum of the areas of its two circular faces is twice the area of the curved surface. What is the volume of the cylinder?


  1. A
    1615 m 3  
  2. B
    1616 m 3  
  3. C
    1617 m 3  
  4. D
    1618 m 3   

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    Solution:

    Given the height of cylinder =10.5m and three times the sum of the areas of its two circular faces is twice the area of the curved surface.
    So,
    3×2π r 2 =2×2πrh 6π r 2 =4πrh 6π r 2 6πr = 4πrh 6πr r= 2 3 h   Put the value of h in the above equation.
    r= 2 3 ×10.5 r= 2 3 × 105 10 r=7  
    So, radius of the cylinder (r)=7m.
    Now, the volume of the cylinder is,
    =π r 2 h = 22 7 × 7 2 ×10.5 = 22 7 ×7×7× 105 10 =1617 m 3    Thus, the volume of the cylinder is 1617 m 3  .
    Therefore, option 3 is correct.
     
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