Find, to the nearest tenth, the lateral area of a cone with a diameter of 40 centimeters and a slant height of 29 centimeters.
Let’s begin by sketching this cone. We know that the diameter of its circular base is 40 centimeters. And its slant height, which is the distance from the apex of the cone to the circumference of the circular base, is 29 centimeters. So the cone looks like this. We’re asked to find the lateral area of the cone. Another way to describe this is as the curved surface area of the cone, the area of its curved face, but not its circular base.
The formula for calculating this area is 𝜋𝑟𝑙, where 𝑟 represents the radius of the base of the cone and 𝑙 is the slant height. We’re given the slant height in the question; it’s 29 centimeters. And we can easily work out the radius by halving the diameter. If the diameter of the cone is 40 centimeters, then the radius is 20 centimeters. The lateral area of the cone is therefore equal to 𝜋 multiplied by 20, for the radius, multiplied by 29, for the slant height, which is 580𝜋.
Now we could leave our answer in this form if we didn’t have a calculator or if we were required to give an exact answer. But as we’ve been asked to give our answer to the nearest tenth, we’ll evaluate this. It is 1,822.123 continuing, which to the nearest tenth is 1,822.1. As this is an area, its units will be square units. And in this case, the units will be square centimeters. The lateral area of this cone, which is its curved surface area, is 1,822.1 square centimeters to the nearest tenth.