Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
If the surface area of the cylinder is 8cm , then the largest possible volume of such cylinder is (16/3)√(2/3π) cubic units .
In the question ,
it is given that ,
the cylinder is an open top ,
given that surface area = 8cm² ,
So , the surface area is = 2πrh + πr²,
8 = 2πrh + πr²
So , h = (8 - πr²)/2πr ,
the volume of the cylinder is (V) = πr²h ,
Substituting the value of h ,
we get ,
V = (8r - πr³)/2,
to find the largest volume , we differentiate it with respect to "r" and equate to 0 ,
we get ,
(8r - πr³)/2 = 0
On Simplifying we get ,
r = √(8/3π) ,
the volume is maximum when r = √(8/3π) ,
So , Volume is = ( 8(√8/3π) - π√(8/3π)³)/2
V = 4(√(8/3π)) - (4/3)(√(8/3π))
V = (8/3)√(8/3π)
V = (16/3)√(2/3π) cubic units .
Therefore , the maximum volume is (16/3)√(2/3π) cubic units .
Learn more about Volume here
https://brainly.com/question/15587628
#SPJ4
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
