📚 Topic Summary
The volume of a square pyramid tells us how much space it occupies. To find it, you need to know the side length of the square base and the height of the pyramid. Think of it like filling the pyramid with water – the volume is the amount of water it would hold.
The formula for the volume of a square pyramid is: $V = \frac{1}{3} * a^2 * h$, where $V$ is the volume, $a$ is the side length of the square base, and $h$ is the height of the pyramid. Remember, the height is the perpendicular distance from the base to the apex (tip) of the pyramid. Let's test your knowledge!
🧮 Part A: Vocabulary
Match the following terms with their definitions:
| Term |
Definition |
| 1. Volume |
A. The distance from the base to the apex of the pyramid. |
| 2. Square Base |
B. A three-dimensional shape with a square base and triangular faces that meet at a point. |
| 3. Height |
C. The amount of space a three-dimensional object occupies. |
| 4. Pyramid |
D. The point at the top of the pyramid. |
| 5. Apex |
E. A polygon with four equal sides and four right angles, forming the base of the pyramid. |
(Answers: 1-C, 2-E, 3-A, 4-B, 5-D)
✏️ Part B: Fill in the Blanks
Complete the following paragraph using the words: volume, base, height, three, square.
The ______ of a square pyramid is the amount of space inside it. It has a ______ shaped ______ and the formula uses the ______ of the pyramid. You also need to divide by ______ to get the correct answer.
(Answers: volume, square, base, height, three)
🤔 Part C: Critical Thinking
Imagine you have two square pyramids. Pyramid A has a base side length of 4 cm and a height of 6 cm. Pyramid B has a base side length of 6 cm and a height of 4 cm. Which pyramid has the larger volume and why?
(Answer: Pyramid B has a volume of 48cm³ while Pyramid A has a volume of 32cm³. Pyramid B has a larger volume.)