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Show that the height of the right circular cylinder of given surface area and maximum volume is equal to the diameter of its base.

Asked by Amal Rajiv 9th January 2014, 3:46 PM
Answered by Expert
Answer:
Please check your question. It should be a closed right circular cylinder.
 
Let r be the radius of the base and h be the height of the cylinder.
 
Let S be the total surface area.
 
Thus,
 
Let Volume of the cylinder be V
 
Thus, we have,
 
Now differentiating the above function with respect to r, we have
 
For maximum, or minimum, we have
 
 
 
But
 
Differentiating with respect to r, we obtain,
 
Hence, V is maximum when h = 2r, i.e. when the height of the cylinder is equal to the diameter of the base.
Answered by Expert 10th January 2014, 11:00 AM
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