You've got a sizable chunk of delicious sharp cheddar. Your block of cheese is a perfect rectangular solid, dimensions are 10in x 13in x 14in.
PLEAASSSEE HELP
You have 10 friends at your house, so you cut 10 slices. Each slice is of width 1in, and it is cut parallel to one face of the cheese. The individual slices are not necessarily parallel to each other.
What is the maximum possible volume (in cubic in) of the remaining block after the 10 slices have been cut off?
To find the maximum possible volume of the remaining block after cutting off 10 slices, we need to determine the orientation of the cuts that would result in the largest remaining volume.
Let's consider the dimensions of the cheese block:
Length (L) = 10 inches
Width (W) = 13 inches
Height (H) = 14 inches
The objective is to maximize the volume after cutting off the slices.
Since the individual slices can be of any width and are not necessarily parallel to each other, we have some flexibility in how the slices are cut.
To maximize the remaining volume, we want to minimize the total area of the cut surfaces. The volume of the remaining block is given by the formula:
Volume = Length * Width * Height
The volume of one slice can be calculated as:
Volume of one slice = Width * Height * Slice Width
Since we want to maximize the remaining volume, we should minimize the total area of the cut surfaces. If we cut the slices parallel to the smallest face (10in x 13in), we minimize the total area of the cut surfaces.
So, the slices should be cut parallel to the 10in x 13in face. Since each slice has a width of 1in, the total area of the cut surfaces would be:
Total area of cut surfaces = Width * Height * Number of Slices
Total area of cut surfaces = 13in * 14in * 10 slices = 1820 square inches
Subtracting this total area of cut surfaces from the volume of the original block gives us the maximum possible volume of the remaining block:
Volume of remaining block = (Length * Width * Height) - (Total area of cut surfaces)
Volume of remaining block = (10in * 13in * 14in) - 1820in^2
Volume of remaining block = 1820 cubic inches
Therefore, the maximum possible volume of the remaining block after cutting off 10 slices is 1820 cubic inches.