Find the volume of the composite figure.
2 in.5 in.8 in.5 in.2 in.
The volume of the composite figure is blank
cubic inches.
To find the volume of a composite figure, we need to break it down into simpler shapes and calculate the volume of each shape separately. Then, we can add up the volumes of all the shapes to find the total volume of the composite figure.
Looking at the given figure, it appears to be a combination of rectangular prisms and triangular prisms.
To start, let's identify the rectangular prisms:
2 in. 5 in. 8 in.
5 in. 2 in.
We have two rectangles with dimensions 2 in. x 5 in. x 8 in. and 5 in. x 2 in. x 5 in.
The volume of a rectangular prism is calculated by multiplying its length, width, and height. So, the volume of the first rectangular prism is 2 in. x 5 in. x 8 in. = 80 cubic inches, and the volume of the second rectangular prism is 5 in. x 2 in. x 5 in. = 50 cubic inches.
Next, let's look at the triangular prisms:
8 in. 5 in.
5 in. 2 in.
We have two triangular prisms with base dimensions 8 in. x 5 in. and 5 in. x 2 in.
The volume of a triangular prism is calculated by multiplying its base area and height and dividing by 2. Since the bases are right triangles, the formula is:
Volume = (base area x height) / 2
The base area of the first triangular prism is calculated as (8 in. x 5 in.) / 2 = 20 square inches. Multiplying the base area by the height (8 in.), we get (20 sq. in. x 8 in.) / 2 = 80 cubic inches for the first triangular prism.
The base area of the second triangular prism is calculated as (5 in. x 2 in.) / 2 = 5 square inches. Multiplying the base area by the height (5 in.), we get (5 sq. in. x 5 in.) / 2 = 12.5 cubic inches for the second triangular prism.
Now, we can add up the volumes of all the shapes to find the total volume of the composite figure:
Total volume = volume of the first rectangular prism + volume of the second rectangular prism + volume of the first triangular prism + volume of the second triangular prism
= 80 cubic inches + 50 cubic inches + 80 cubic inches + 12.5 cubic inches
= 222.5 cubic inches
Therefore, the volume of the composite figure is 222.5 cubic inches.
cubes, pyramids, cones, spheres?
You don't give much to go on.