Question

A composite figure has numbers of 7 in, 7 in, 7 in, 10 in, 8 in, and 16 in. what is the volume of the figure?

Answer 1

To find the volume of the composite figure, we need to first identify the individual figures that make up the composite figure.

From the given dimensions, we have:
- A cube with sides of 7 inches
- A cube with sides of 10 inches
- A cube with sides of 8 inches
- A rectangular prism with dimensions 16 inches by 7 inches by 7 inches

The volume of a cube is calculated by V = s^3, where s is the length of a side.
So, the volumes of the cubes are:
- Cube with sides of 7 inches: V1 = 7^3 = 343 cubic inches
- Cube with sides of 10 inches: V2 = 10^3 = 1000 cubic inches
- Cube with sides of 8 inches: V3 = 8^3 = 512 cubic inches

The volume of a rectangular prism is calculated by V = l * w * h, where l is the length, w is the width, and h is the height.
So, the volume of the rectangular prism is:
- Rectangular prism with dimensions 16 inches by 7 inches by 7 inches: V4 = 16 * 7 * 7 = 784 cubic inches

Now, we can find the total volume of the composite figure by adding the volumes of the individual figures:
Total Volume = V1 + V2 + V3 + V4
Total Volume = 343 + 1000 + 512 + 784 = 2639 cubic inches

Therefore, the volume of the composite figure is 2639 cubic inches.