Find the volume, in cubic inches, of the composite solid below, which consists of a 4 -inch square solid rectangular bar that is 16 inches in length. The bar has a 2-inch diameter cylinder hole cut out of the center of the bar from the top of the bar through the entire length of the bar. Use pi= 3.14 to find the volume. Enter only the number.
An image shows a solid rectangular metal bar that has a 4-inch square top and a length of 16 inches. There is a 2-inch diameter cylinder hole cut out of the center of the bar from the top to the bottom of the bar.
The solution is
To find the volume of the composite solid, we need to calculate the volumes of the rectangular bar and the cylinder hole separately and then subtract the volume of the hole from the volume of the bar.
The volume of the rectangular bar is given by the formula V = lwh, where l is the length, w is the width, and h is the height. In this case, the length is 16 inches, the width is 4 inches, and the height is 4 inches (since the square top has the same dimensions as the width). Thus, the volume of the rectangular bar is V = 16 * 4 * 4 = 256 cubic inches.
The volume of the cylinder hole is given by the formula V = πr^2h, where r is the radius and h is the height. In this case, the radius is half the diameter, so r = 2/2 = 1 inch. The height is the same as the length of the rectangular bar, so h = 16 inches. Thus, the volume of the cylinder hole is V = 3.14 * (1^2) * 16 = 50.24 cubic inches.
To find the volume of the composite solid, we subtract the volume of the cylinder hole from the volume of the rectangular bar: 256 - 50.24 = 205.76.
Therefore, the volume of the composite solid is approximately 205.76 cubic inches.