Show how to slice a cylindrical piece of cheese into
eight congruent pieces with three slices.
Think of symmetry about the x-, y- and z-axes.
To slice a cylindrical piece of cheese into eight congruent pieces using three slices, follow these steps:
Step 1: Visualize the cylindrical piece of cheese.
Imagine a cylindrical shape, like a round cheese wheel or a piece of salami.
Step 2: Plan your slices.
For this task, you'll need three slices. Let's label them as Slice A, Slice B, and Slice C. Slice A will be the first slice, Slice B the second, and Slice C the third.
Step 3: Position the first slice (Slice A).
Place Slice A anywhere perpendicular to the base of the cylinder. This means the slice should cut straight across the cylindrical piece, dividing it into two equal-sized portions. The result is a top half and a bottom half.
Step 4: Position the second slice (Slice B).
Take Slice B and, at a different angle from Slice A, insert it through one of the cut faces created by Slice A. The second slice should pass through both halves of the cylinder and cut them into two equal-sized pieces each. The result will be four equal-sized quarters.
Step 5: Position the third slice (Slice C).
Now, take Slice C and insert it through one of the other cut faces created by Slice A, but this time at a different angle from Slice B. Like Slice B, Slice C should pass through both halves of the cylinder, as well as the previous quarters. The result will be eight congruent pieces.
Step 6: Adjust and refine if needed.
After executing the three slices, you should have eight equal-sized pieces. However, the slices may need slight adjustments to ensure they are perfectly congruent. If necessary, you can make small tweaks to achieve congruent pieces.
By following these steps and positioning the three slices in the correct manner, you can successfully slice a cylindrical piece of cheese into eight congruent pieces.