Of all the closed cylindrical cans (right circular), of a given volume of 100 cubic centimetres, find the dimensions of the can which has the minimum surface area?

Answer

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Video Transcript

the solution to the question is considered X. With the radius of the circular base and why with the height of the closed right circular cylinder. So formula of total surface area as will be equal to to buy into X. Y plus two by X. Square. And so X. Y plus excess square will be equal to has by to buy equals two K. Now X equals two K minus x square. So why will be called to k minus X square by exploited with the question one. Now the volume of this lender let it with jet is given by pi into excess square into white. So it will be pi X square into k minus X square by X. So that will be equal to pi attacks into k minus X. Square equals two pi into K X minus X cube. So they said by dX will be called to pie into k minus three X squared. Now moving forward there this will be these are the squared by the X squared equals two pi into minus six X. Now dessert by dX must wait for 20 So you will get your ex. Well louis route Gay by three. No ACT X equals to root K by three Days squares Set by dx square will be equal to minus 65 into road. Okay by three which is negative so at X equals to root K by three. That is maximum. Now why is equal to k minus K by three by route A by three. So from the question one from equation one X will be equal to uh two and two Route K by three which is two X. Which implies height as a coolant to the diameter. Therefore the volume of a cylinder is maximum when height is equal to the diameter of its base. Thank you.

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