Final answer:
Amanda's cube with a volume of 4 cubic feet has sides approximately 19.04 inches long. Since this exceeds the 12-inch height of the bookshelf, the cube will not fit.
Step-by-step explanation:
The question at hand involves determining whether Amanda's strong cube, with a volume of 4 cubic feet, will fit on a bookshelf that is 12 inches tall. To answer this, we first need to find the length of the sides of the cube. The volume of a cube is calculated by cubing the length of one of its edges. So we take the cube root of 4 cubic feet to get the length of each side, which equals 1.587 feet, or approximately 19.04 inches (since 1 foot equals 12 inches).
Since the cube's side of approximately 19.04 inches is greater than the height of the bookshelf, which is 12 inches, it follows that the cube will not fit on the bookshelf. Therefore, the correct answer is B. No, the cube will not fit.