Final answer:
To find the volume of the composite solid, calculate the volumes of each individual component (rectangular prism, cube, cylinder) and then add them together. The volume of the composite solid is approximately 986.57 cubic inches.
Step-by-step explanation:
The volume of a composite solid can be found by finding the volumes of each individual component and then adding them together.
In this case, the composite solid is made up of several different shapes: a rectangular prism measuring 10 in by 8 in by 4 in, a cube measuring 3 in on each side, and a cylinder with a height of 6 in and a radius of 6 in.
To find the volume of the rectangular prism, use the formula volume = length x width x height. Substitute the values to find the volume = 10 in x 8 in x 4 in = 320 in³.
To find the volume of the cube, use the formula volume = side³. Substitute the value to find the volume = 3 in³.
To find the volume of the cylinder, use the formula volume = π x radius² x height. Substitute the values and find the volume = π x 6 in² x 6 in = 216π in³.
Add the volumes of each component together to find the volume of the composite solid: 320 in³ + 3 in³ + 216π in³.
Approximately, the volume of the composite solid is 986.57 in³.