Question

A homemade loaf of bread turns out to be a perfect cube. Five slices of bread, each 0.6 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?

Answer 1

A cube has all sides of equal length.

So let the side be x

that will be length = width = height = x  

Now, when we cut the loaf into 5 equal slices, the length and height of the slices are the same as the original loaf.  But the width will become less with each slicing. Here the width corresponds to the thickness of the slices.

For each slice the dimensions are -

Length = x

height = x

width = 0.6

Volume of the original loaf is x³.

Volume of  5 slices is 5(x * x * 0.6).  

Volume that is left after the cutting the slices is 235 inch³.

So, equation of the volume is=

x³ - 5(0.6x²) = 235

Solve for x using this equation.

x³ - 3x² = 235

x³ - 3x² - 235 = 0

Using a graph calculator to find the roots, we get

x = 7.35

Hence the dimensions of the original loaf is 7.35 inches for each side.

Please find attached the graph.