To find the volume of the composite figure, we will need to find the volume of the left and right figures separately and then take the sum. The figure is composed of a half cylinder and a prism. Let's start by finding the volume of the right figure using the formula for the volume of a half cylinder.
V=1/2 π r^2 h
The diameter of the cylinder is equal to the length of the rectangular base, which is 12 inches. Because the radius of a circle equals half the diameter, this implies r= 6 inches. Furthermore, the height of the cylinder is equal to the width of the rectangular base, 10 inches. Let's substitute these values to find the volume of the right figure.
The volume of the right figure is 180 π cubic inches. To find the volume of the left figure, we will use the formula for the volume of a prism.
V=B * h, where B is the area of the base
The base is in the shape of a rectangle. Using the formula for the area of a rectangle, the formula for volume of the prism is as follows.
V=B * h ⇔ V= ( l * w) * h
Looking at the prism, we can see the height is equal to 24 inches. Furthermore, the length of the base is 12 inches and the width is 10 inches. Let's substitute these values into the formula to find the volume of the left figure.
