๐ Topic Summary
The volume of a prism and a pyramid are related when they share the same base area and height. Specifically, the volume of a pyramid is one-third the volume of a prism with the same base and height. Understanding this relationship helps in calculating and comparing the volumes of these two shapes efficiently. This is a fundamental concept in geometry and is used in various real-world applications, from architecture to engineering.
Imagine you have a prism and a pyramid that perfectly fit together. If you could fill the pyramid with water and pour it into the prism, you'd need to fill the pyramid three times to completely fill the prism. This illustrates the 1/3 relationship. Let's practice with some exercises!
๐ค Part A: Vocabulary
| Term |
Definition |
| 1. Volume |
a. A three-dimensional shape with two parallel bases that are congruent polygons. |
| 2. Prism |
b. The amount of space a three-dimensional object occupies. |
| 3. Pyramid |
c. Having the same size and shape. |
| 4. Congruent |
d. A three-dimensional shape with a polygonal base and triangular faces that meet at a common vertex. |
| 5. Height |
e. The perpendicular distance from the base to the top of a shape. |
Instructions: Match each term with its correct definition.
โ๏ธ Part B: Fill in the Blanks
The volume of a ______ is one-third the volume of a ______ with the same base and height. If a prism has a volume of 60 cubic cm, a pyramid with the same base and height will have a volume of ______ cubic cm. Therefore, the formula for the volume of a pyramid is $V = \frac{1}{3} * B * h$, where B is the ______ area and h is the ______.
๐ค Part C: Critical Thinking
Explain in your own words why the volume of a pyramid is one-third the volume of a prism with the same base and height. Provide a real-world example where understanding this relationship might be useful.