Exercise 19 Page 637

We want to find the lateral area of the given cone.

To do so, we must know that the lateral area of a right cone is half the product of the circumference of the base and the slant height. In this formula, $r$ is the radius and $\ell$ is the slant height of the cone. Since we know that the diameter $d$ is equal to $8,$ we can divide it by $2$ and get the radius of the base. With this information we are able to calculate the lateral area of the cone. To do so, we will substitute $r=4$ and $\ell =5$ into the formula for the lateral area. Let's do it! The lateral area of the given cone, to the nearest tenth, is $62.8$ square meters.