Question

The cost of constructing a wooden box with a square base varies jointly as the height of the box and the square of the width of the box. A box of height 16 inches and of width 6 inches costs $28.80. How much would a box of height 14 inches and of width 8 inches cost?

Answer 1

Let cost be C, height h and width w, hence, \[C = k. h.w ^{2}\]
Now putting C= 28.80, h = 16 and w = 6, we get k = 0.05
Hence \[C = 0.05* h.w ^{2}\]
Putting h=14 and w = 8 gives us C = $44.80