the cost of making a box with a square base varies jointly as the height of the box and the square of the width of the box.?

The cost varies jointly as the height of the box and the square of the width.

Let: c = cost
Let: h = height
Let: w = width
Let: k = constant.

Your equation is:

c = khw² (goes up as the height goes up and goes up as the width, squared, goes up).

So you are told if the height is 16 and the width is 6, it costs $28.80. You can use this information to find your constant:

28.8 = k(16)(6)²
28.8 = 16k * 36
28.8 = 576k
28.8 / 576 = k

No need to reduce it since we're just going to use it right away. Using this constant and the same equation, what is the cost of a 14" height and 8" width box.

c = khw²
c = (28.8/576)(14)(8)²
c = (28.8/576)(14)(64)
c = 25804.8/576
c = 44.8

The cost will be $44.80.