Dimension of trash bin is 6 ft x 6 ft x 3ft .
Explanation:
Let h be the height of box and a be the side of base square.
We have 108 ft² material.
Surface area of trash bin = 108 ft²
Surface area of trash bin = a² + 4 ah
a² + 4 ah = 108
4ah = 108 - a²

Volume of trash bin, V = a²h

At maximum volume differentiation of volume will be zero

Surface area of trash bin = a² + 4 ah = 108
36 + 4 x 6 x h = 108
h = 3 ft
Dimension of trash bin is 6 ft x 6 ft x 3ft .