Q. 175.0( 2 Votes )

<span lang="EN-US

Answer :

Let the length, width and height of the open tank be x, x and y units respectively. Then, its volume is and the total suface area is .

It is given that the tank can hold a given quantity of water. This means that its volume is constant. Let it be V.


The cost of the material will be least if the total surface area is least. Let S denote the total surface area.


We have to minimize S object to the condition that the volume V is constant.


Differentiating w.r.t x, we get,

Differentiating again w.r.t x, we get,

The critical numbers of S are given by


x = 2y


 > 0, for all x

Hence, S is minimum when x = 2y, i.e. the depth (height) of the tank is half of its width.

Value – In the above mentioned question, the values that are being shown are of care, concern towards the weaker section of society.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses

If the sum of theMathematics - Board Papers

A metal box with Mathematics - Board Papers

Show that aRD Sharma - Volume 1

Find the local maMathematics - Board Papers

Prove that the seMathematics - Board Papers

Prove that the raMathematics - Board Papers

Prove that the leMathematics - Board Papers