Exercise 38 Page 723

The volume of the remaining solid will be the difference between the volumes of the prism and the cylinder cut-out. We will start by finding the volume of the prism. Let's recall the formula. V= B * h, where B is the area of the base The base is in the shape of a square. Using the formula for the area of a square, the formula for the volume of the prism is as follows. V= B * h ⇔ V= s^2 * hWe are given that the side lengths of the base are 6 inches and the height of the prism is 6 inches. Let's substitute these values to find the volume of the prism.

The volume of the prism is 216 cubic inches. To find the volume of the cylinder cut-out, let's recall the formula for the volume of a cylinder. V= π r^2 h We are given the diameter of 5 inches. The radius is equivalent to half of the diameter, which implies r= 52 inches. Furthermore, we can see the height of the cylinder is 6 inches. Let's substitute these values into the formula to find the volume.

The volume of the cylinder is about 117.8 cubic inches. Finally, we will take the differences of the two volumes to find the volume of the remaining solid. V_(Remaining solid)=V_(Prism)-V_(Cylinder) ⇕ V_(Remaining solid)=216-117.8=98.2 in.^3 The volume of the remaining solid is approximately 98.2 cubic inches.