Problem 38 - Contemporary Precalculus

Question

A homemade loaf of bread turns out to be a perfect cube. Five slices of bread, each .6 inch thick, are cut from one end of the loaf. The remainder of the loaf now has a volume of 235 cubic inches. What were the dimensions of the original loaf?

Step-by-Step Solution

Answer

Answer: The dimensions of the original cubic loaf of bread are approximately 6.44 inches by 6.44 inches by 6.44 inches.

Step 1: Let x be the side length of the original loaf

Let x inches be the side length of the original cubic loaf of bread. So, the volume of the original loaf is x^3 cubic inches.

Step 2: Calculate the total thickness of the slices cut off

We know that five slices of bread, each 0.6 inch thick, are cut off from the loaf. Therefore, the total thickness of the slices cut off is 5 * 0.6 = 3 inches.

Step 3: Calculate the side length of the remainder loaf

The loaf was originally a perfect cube, and when the slices were removed, it became slightly shorter but remained cubic in shape. So, the side length of the remainder loaf is (x - 3) inches.

Step 4: Write the equation for the volume of the remainder loaf

The volume of the remainder loaf is 235 cubic inches. Therefore, we can set up the equation for the volume of the remainder loaf: (x - 3)^3 = 235

Step 5: Solve the equation for x

Now we need to solve the equation (x - 3)^3 = 235 for x. Taking the cube root of both sides, we get x - 3 = \sqrt[3]{235}. Adding 3 to both sides, we get x = 3 + \sqrt[3]{235}.

Step 6: Calculate the dimensions of the original loaf

Using a calculator, we find that x is approximately 6.44 inches. Since the original loaf was a perfect cube, its dimensions were 6.44 inches by 6.44 inches by 6.44 inches.