Explain why a cross section of a polyhedron does not always match the base of that polyhedron.
1 answer:
Explanation:
If the polyhedron is a prism and the cross sections are parallel to the base, then the cross section will match the base. Under other conditions, the cross section may not match the base.
For example, the first attachment is a figure of a cube. Cross sections are shown that have the shape of a triangle, trapezoid and hexagon. Other cross sections are possible.
A general polyhedron need not be regular and need not have any cross section congruent to the base (except the cross section that <em>is</em> the base). For some polyhedrons, it may be difficult even to identify the base. See the second attachment.
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9514 1404 393
Answer:
- 113.04, 4, 452.16
- 78.5, 11, 863.5
- 153.86, 10, 1538.6
Step-by-step explanation:
When calculations are repetitive, I like to let a calculator or spreadsheet do them. Here we have used the formula for the base area:
B = πr² = 3.14×r²
In the second figure, the radius is half the diameter, so is 5 units.
The table in the attachment lists the base area B, the height h (from the figures), and the volume V. These are the values that you need to drag and drop to the boxes in your problem.
V = 113.04 · 4
V = 452.16 units³ . . . showing how the numbers are used in the first figure
