In this lesson, we will learn how to find the volume of composite 3D figures. A composite figure is made up of two or more simpler shapes put together. To find the volume of a composite figure, we need to break it down into its simpler shapes and then calculate the volume of each shape separately.
Let's walk through an example to illustrate this concept:
Example:
Find the volume of the following composite figure:
[insert image of composite figure]
Solution:
First, let's break down the composite figure into simpler shapes. In this case, the figure consists of a rectangular prism and a pyramid.
Step 1: Find the volume of the rectangular prism
The rectangular prism has a length of 8 units, a width of 4 units, and a height of 6 units. To find the volume of a rectangular prism, we use the formula:
Volume = length x width x height
Volume = 8 x 4 x 6
Volume = 192 cubic units
Step 2: Find the volume of the pyramid
The pyramid has a base that is a rectangle with a length of 8 units and a width of 4 units, and a height of 6 units. To find the volume of a pyramid, we use the formula:
Volume = 1/3 x base area x height
Base area = length x width = 8 x 4 = 32 square units
Volume = 1/3 x 32 x 6
Volume = 64 cubic units
Step 3: Add the volumes of the rectangular prism and the pyramid together
Volume of composite figure = volume of rectangular prism + volume of pyramid
Volume = 192 + 64
Volume = 256 cubic units
Therefore, the volume of the composite figure is 256 cubic units.
By breaking down composite figures into simpler shapes and calculating their volumes individually, we can easily find the volume of the entire composite figure. Practice with more examples to strengthen your understanding of finding the volume of composite 3D figures.
UNIT 7 Volume LESSON 7 Volume of Composite 3D Figures
1 answer
9 answers