Unit 7 lesson 7 volume of composite 3D figures
Solve for the volume of the composite figure.
To solve for the volume of a composite figure, you will need to break down the figure into simpler shapes and calculate the volume of each individual shape. Then, you can add up the volumes of all the shapes to find the total volume of the composite figure.
Here is an example of a composite figure and how to calculate its volume:
Suppose you have a composite figure made up of a rectangular prism and a cylinder. The dimensions of the rectangular prism are length 6 cm, width 4 cm, and height 3 cm. The dimensions of the cylinder are radius 2 cm and height 6 cm.
First, calculate the volume of the rectangular prism:
Volume = length x width x height
Volume = 6 cm x 4 cm x 3 cm
Volume = 72 cm³
Next, calculate the volume of the cylinder:
Volume = πr²h, where r is the radius and h is the height
Volume = π(2 cm)² x 6 cm
Volume = π(4 cm²) x 6 cm
Volume = 24π cm³ or approximately 75.4 cm³
Now, add up the volumes of the rectangular prism and the cylinder to find the total volume of the composite figure:
Total volume = Volume of rectangular prism + Volume of cylinder
Total volume = 72 cm³ + 24π cm³
Total volume = 72 cm³ + 75.4 cm³
Total volume = 147.4 cm³
Therefore, the volume of the composite figure is approximately 147.4 cm³.