Final answer:
To find the volume of the composite figure, calculate the volume of the cylinder and rectangular prism separately, then add the volumes together.
Step-by-step explanation:
To find the volume of the composite figure, we need to find the volume of the cylinder and the rectangular prism, and then add them together.
For the cylinder, we can use the formula V = πr²h. Given the radius r = 3 in. and the height h = 5 in., we can calculate the volume as V = 3.142 × (3 in.)² × 5 in. = 141.21 in³.
For the rectangular prism, we can use the formula V = lwh. Given the length l = 10 in., width w = 4 in., and height h = 12 in., we can calculate the volume as V = 10 in. × 4 in. × 12 in. = 480 in³.
Finally, we add the volumes of the cylinder and rectangular prism to get the total volume of the composite figure: 141.21 in³ + 480 in³ = 621.21 in³.