Exercise 21 Page 818

We are asked to find the lateral area and surface area of the given cylinder.

We will do these things one at a time.

Lateral Area

Let's recall the formula for the lateral area L of a right cylinder. L=2π rh Here, r is the radius of the base, and h is the height of the cylinder. We will start by finding the radius of the base. In the diagram, we see that the base is a circle with diameter equal to 8in. Its radius is exactly the half of the length of the diameter. r = 8/2 ⇒ r = 4 We also see in the diagram that the height of the solid is 6.2in. With this information, we can find the lateral area of the prism.

The lateral area of the solid is 49.6 π in^2 that is approximately 155.8 in^2.

Surface Area

Let's recall the formula for the surface area of a cylinder. S=L+2π r^2 In this formula, r is the radius of the base and L is the lateral area of the cylinder. Substituting r with 4 and L with 49.6 π into the formula, we can calculate S. Let's do it!

The surface area of the cylinder is about 256.4 in^2.