Please can someone help me with these last few questions on my homework? You don't have to give an answer because I would very much like to know how to do them?

Question

An open box is formed by cutting squares with side lengths of 3 inches from each corner of a square piece of paper. What is a side length of the original paper if the box has a volume of 675 cubic inches?

21 inches

24 inches

33 inches

36 inches

The weekly cost (C) of growing and selling x acres of flowers is approximated by C = 0.2x2 12x + 240. How many acres of flowers would minimize these costs?

10 acres

20 acres

30 acres

60 acres

Answer 1

If the box originally had side s, then the new box has side s-6, since 3" was cut off each corner. The height of the box is just the 3" that was cut off. So,

s(s-6)^2 = 675
Now, just by inspection, 675 = 3*225 = 3*15^2

So, the box now has sides of 15, and height=3

The original paper was thus 21" on a side.