Answer:
Dimensions 30 in x 30 in x 15 in
Surface Area = 2,700 in²
Explanation:
Let 'r' be the length of the side of the square base, and 'h' be the height of the bin. The volume is given by:

The total surface area is given by:

Rewriting the surface area function as a function of 'r':

The value of 'r' for which the derivate of the surface area function is zero, is the length for which the area is minimized:
![A=54,000*r^(-1)+r^2\\(dA)/(dr)=0= -54,000*r^(-2)+2r\\(54,000)/(r^2)=2r\\ r=\sqrt[3]{27,000}\\r=30\ in](https://img.qammunity.org/2021/formulas/mathematics/college/n5zxgqi5qema8dv4v8mn1dl1dne8eqlt2y.png)
The value of 'h' is:

The dimensions that will ensure the minimum surface area are 30 in x 30 in x 15 in.
The surface area is:
