We know that the volume of a rectangular tank with a square base is going to be X * X * y, and we're told that the total volume is 5324. So we can solve for Y, giving us 5324 / X ^2. The surface area of this open rectangular tank is going to be the base X * X or X ^2 plus four of the sides, and the sides are X * y. So instead of the Y, if we put in 5324 / X ^2 and simplify, we had our surface area equaling X ^2 + 21,296 / X. Taking the first derivative and setting it equal to 0, we get 0 equaling two X -, 2000 twenty 1296 / X ^2. Solving for X we get X equal 22. To get Y, we're going to just substitute it back in 5324 / 22 ^2 is going to give us 11. So the dimensions of the tank 22 by 22 by 11.