In this concept, you will learn to calculate the volume of pyramids.
Volume is the measure of how much space a three-dimensional figure takes up or holds. Imagine a funnel. The funnel’s size will determine how much water the funnel will hold. If you fill it with water, the amount of water tells the volume of the funnel. Volume is often what you think of when you talk about measuring liquid or liquid capacity. Note that you measure volume in cubic units.
Pyramids are unusual because they are so much smaller at the top than they are at their base. The important thing to remember is that measuring volume involves filling up a solid figure. A pyramid has exactly one-third the volume of a cube.
The formula for finding the volume of pyramids is:
Here are some common area formulas:
Let’s look at an example.
What is the volume of the pyramid below?
Earlier, you were given a problem about Brianna’s melting gift.
Then, find the number of hours the candle will burn.
The answer is 57.6.
The candle will burn 57.6 hours.
First, substitute what you know into the formula for the volume of the pyramid.
The answer is 19.
The answer is 40.33.
The answer is 128.
The answer is 240.
Answer each of the following questions.
1. What is the formula that you would need for finding the volume of a pyramid?
2. When you see a capital B in a formula it means that you are looking for the perimeter or area of the base?
3. What is the name of the figure pictured below?
4. What is the shape of the base?
5. What is the volume of the figure?
6. What is the name of the figure pictured above?
7. What is the difference between this figure and the last figure?
8. What is the volume of this figure?
9. What is the shape of the base?
Use what you have learned to solve each of the following problems.
10. A square pyramid has a base with sides of 6 yards each and a volume of 175 cubic yards. What is its height?
11. Claire has a perfume bottle shaped like a triangular pyramid. Its base area is 48 square centimeters, and its height is 28 centimeters. How much does the bottle hold when it is exactly half full?
12. Find the volume of a square pyramid with a base of 4 inches and a height of 6 inches.
13. Find the volume of a rectangular pyramid with a length of 5 inches, a width of 7 inches and a height of 8 inches.
14. Find the volume of a square pyramid with a base of 8 meters and a height of 12 meters.
15. Find the volume of a square pyramid with a base of 13.5 meters and a height of 15 meters.
To see the Review answers, open this PDF file and look for section 8.12.