Exercise 16 Page 872

Consider the given solid.

The given solid is a cylinder. It has a radius of 4 inches and a height of 5 inches. Let's first calculate the lateral area and then the surface area.

Lateral Area

To calculate the lateral area, we can use the known formula where h is the height of the cylinder and r is the radius of the base. L=2π rh We are given both the height and the radius. Let's calculate the lateral area.

The lateral area is about 125.7 square inches.

Surface Area

To calculate the surface area of a cylinder, we can use the known formula where h is the height of the cylinder and r is the radius of the base. S=2π rh+2π r^2 Earlier, we found that 2π r h is about 125.7. Moreover, we have that r is 4. Let's substitute these values into the formula and calculate S.

The surface area of the cylinder is about 226.2 square inches.