Exercise 6 Page 849

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. Let's start by finding the radius of the base. In the diagram, we see that the base is a circle with diameter equal to 20.4cm. Its radius is exactly the half of the length of the diameter. r = 20.4/2 ⇒ r = 10.2 We also see in the diagram that the height of the solid is 22cm. With this information, we can find the lateral area of the prism.

The lateral area of the cylinder is 1409.9cm^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 10.2 and L with 1409.9 into the formula, we can find the value of S. Let's do it!

The surface area of the cylinder is about 2063.6 cm^2.