Exercise 30 Page 648

The given solid is a cone with a diameter of $16.5$ feet and a slant height of $9.5$ feet. To calculate the lateral area, 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. We know that the diameter of the cone's base is $16.5$ feet. By dividing by $2,$ we get the radius of the base. We now know that the radius of the cone is $8.25\text{ ft}$ and that the slant height of the cone is $9.5\text{ ft}.$ With this information we are able to calculate the lateral area of the cone. To do so, we will substitute $r=8.25$ and $\ell =9.5$ into the formula for the lateral area. Let's do it! The lateral area of the given cone, rounded to the nearest tenth, is $246.2{\text{ ft}}^2.$