Question

In a park, an open tank is to be constructed using metal sheet with a square base and vertical sides so that it contains 500 cubic meters of water. using above information answer the following:

find the minimum surface area of the tank.

Answer 1

To find the minimum surface area of an open tank with a square base that can hold 500 cubic meters of water, one must calculate the dimensions of the base and height that minimize surface area given the volume, then calculate that minimized surface area.

Step-by-step explanation:

The student is tasked with finding the minimum surface area of an open metal tank with a square base that can contain 500 cubic meters of water. To find the minimum surface area, the dimensions of the tank that minimize the surface area for the given volume must be calculated. If x is the length of one side of the base and h is the height of the tank, from the given volume we get x2h = 500. The surface area S of the tank is x2 + 4xh.

To find the minimum surface area, we differentiate S with respect to x and set the derivative equal to zero. We then solve for x, substitute it into the equation for h to find its value, and finally, calculate the surface area using these dimensions.