This Composite Figure Is Made Of Two Identical Pyramids Attached At Their Bases. Each Pyramid Has A Height Of 2 Units.Which Expression Represents The Volume, In Cubic Units, Of The Composite Figure?A.
**Understanding the Composite Figure: A Mathematical Exploration**
What is the Composite Figure?
The composite figure is a three-dimensional shape made up of two identical pyramids attached at their bases. Each pyramid has a height of 2 units, and the base of each pyramid is a square with side length 4 units.
What is the Volume of the Composite Figure?
The volume of a pyramid is given by the formula: V = (1/3) * base area * height. Since the base of each pyramid is a square with side length 4 units, the base area is 4^2 = 16 square units. The height of each pyramid is 2 units.
How to Find the Volume of the Composite Figure?
To find the volume of the composite figure, we need to find the volume of one pyramid and then multiply it by 2, since there are two identical pyramids.
Step 1: Find the Volume of One Pyramid
Using the formula for the volume of a pyramid, we can find the volume of one pyramid:
V = (1/3) * base area * height = (1/3) * 16 * 2 = (1/3) * 32 = 10.67 cubic units
Step 2: Find the Volume of the Composite Figure
Since there are two identical pyramids, we can multiply the volume of one pyramid by 2 to find the volume of the composite figure:
V = 2 * 10.67 = 21.33 cubic units
What is the Expression that Represents the Volume of the Composite Figure?
The expression that represents the volume of the composite figure is:
V = 2 * (1/3) * 4^2 * 2
Simplifying the Expression
We can simplify the expression by evaluating the exponent and multiplying the numbers:
V = 2 * (1/3) * 16 * 2 = 2 * (1/3) * 32 = 2 * 10.67 = 21.33 cubic units
Conclusion
In conclusion, the expression that represents the volume of the composite figure is V = 2 * (1/3) * 4^2 * 2. This expression can be simplified to V = 21.33 cubic units, which is the volume of the composite figure.
Frequently Asked Questions
Q: What is the base area of each pyramid?
A: The base area of each pyramid is 4^2 = 16 square units.
Q: What is the height of each pyramid?
A: The height of each pyramid is 2 units.
Q: How to find the volume of the composite figure?
A: To find the volume of the composite figure, we need to find the volume of one pyramid and then multiply it by 2, since there are two identical pyramids.
Q: What is the expression that represents the volume of the composite figure?
A: The expression that represents the volume of the composite figure is V = 2 * (1/3) * 4^2 * 2.
Q: Can we simplify the expression?
A: Yes, we can simplify the expression by evaluating the exponent and multiplying the numbers.
Q: What is the volume of the composite figure?
A: The volume of the composite figure is 21.33 cubic units.
Q: How to find the volume of the composite figure using the formula?
A: To find the volume of the composite figure using the formula, we need to use the formula for the volume of a pyramid and multiply it by 2, since there are two identical pyramids.
Q: What is the formula for the volume of a pyramid?
A: The formula for the volume of a pyramid is V = (1/3) * base area * height.
Q: Can we use the formula to find the volume of the composite figure?
A: Yes, we can use the formula to find the volume of the composite figure by substituting the values of the base area and height into the formula.