What whole number dimensions would allow the students to maximize the volume while keeping the surface area at most 160 square feet

The whole number dimension that would allow the student to maximize the volume while keeping the surface area at most 160 square is 6 ft

Step-by-step explanation:

Here we are required find the size of the sides of a dunk tank (cube with open top) such that the surface area is ≤ 160 ft²

For maximum volume, the side length, s of the cube must all be equal;

Therefore area of one side = s²

Number of sides in a cube with top open = 5 sides

Area of surface = 5 * s² = 180

Therefore s² = 180/5 = 36

s² = 36

s = √36 = 6 ft

Therefore, the whole number dimension that would allow the student to maximize the volume while keeping the surface area at most 160 square = 6 ft.