 In this video, practice problem 2, we're told the sugar cone has an altitude of 8 inches and a diameter of 2.5 inches and we're asked to find the approximate lateral area of the sugar cone. Couple things to note when you're doing these problems is always look to see if you're asked to find the approximate or the exact value. This one we're asked to find the approximate value so we know our final answer is going to be in decimal form, not pi form. Look to see if you're asked to find the total surface area or the lateral area. In this case, we're asked to find the lateral area. So when I pull up my surface area formula for a cone, which you should be familiar with by now, pi RL plus pi R squared, keep in mind if we're only going to find the lateral area, we're going to take off the pi R squared because that pi R squared represents the area of my base, the area of the circle and we only want to find the lateral area. So I'm going to write that out as my new formula of a lateral area and I'm just going to have a basic cone here so I can label my pieces. Let's first look at what information is given to us and label our figure. We have an altitude of 8 inches and a diameter of 2.5 inches. It's a good idea to draw a cone and put all the information in that we know. So we know the altitude is 8 inches. The altitude, remember, is that vertical piece that's perpendicular to the base coming from the top or bottom point of that cone. That's going to be that perpendicular piece. I can even put a little right angle symbol there that will help us later. And we're told that the diameter is 2.5 inches. So be careful when you're given information. The diameter is 2.5, but I want to label just the radius. So if the diameter is 2.5, my radius is half of that, which is 1.25. And next, before I begin, I'm just going to write down the values that I need for my formula. All I need is the radius and the L, which represents the slant height. So I'm going to write that off to the side down here. I know now that my radius is 1.25, but my slant height is represented by the hypotenuse of this right triangle. 8 is not the slant height. 8 is going to be your altitude. So I'm going to have to do some work to find the slant height. And you'll notice that's why I put this right angle symbol in there to show that if this is a right triangle, I can find the slant height using the Pythagorean theorem. So if I'm trying to find this value, my slant height, I'm just going to set up the Pythagorean theorem off to the side here. 8 squared plus 1.25 squared equals x squared. That's the hypotenuse by itself. And when I go ahead and simplify that, you'll need your calculator. 1.25 squared is 1.5625. And now you'll see why we needed the approximate value for our final answer. Because we are going to be getting some decimals here. Equals x squared. When I simplify that, I get x squared equals 65.5625. It's important not to round. And when we take the square root of that, we're going to take the square root of both sides to solve for x. We get x equals 8.097. And we're not told what to round to on this one. But I'll tell you we're going to round our final answer to the nearest tenth. And we would be told that when we're doing homework or if we're doing a quiz or a test, we'd be very specific about that. And so when I round x equals 8.097, I'm going to put my slant height in as a value of 8.1 would be rounded to the nearest tenth. Now that I have the values, I can plug those into the formula for the lateral area. And I get lateral area equals pi times my radius times my slant height. And remember, because we want the approximate value, this is when you are going to use the pi button when we plug this all into the calculator. Plug in pi times 1.25 times 8.1. And it's important to use the pi button when you're calculating this and not round it to 3.14 until the end. When I plug that all in, I get 31.8086. And it goes on and on. I want to round, remember, to the nearest tenth. So my final answer, my lateral area of the sugar cone is 31.8. And because it is an area, I'm going to label that not units. We're told it's inches squared is my final answer.