Hi, I'm Rebecca Pierce for About.com and today we're going to be talking about the surface area of a cone.

Find the Parts of a Cone

So first let's look at a diagram of a cone. We have a side length, which we're going to call S, which is the diagonal of the cone. We also have a base which is the circle at the bottom. On the circle we have labeled R, which is your radius. And your radius is just a line from one side of the circle to the center of the circle. In this diagram, we also have labeled h, which is the height of your cone. And you may or may not need to use the height in some problems.

Learn the Formula for Surface Area of a Cone

We're going to break the surface area formula into two parts. The first part is the area of the base, which as we said before, is the circle at the bottom of the cone. And the area of a circle is πr2. The second part of the surface area formula is the area of the actual conical section. And the area of a cone is πrs, where s is the side length and r is the radius. So to get the total area, we simply add the area of the base to the area of the conical section. So we have A = πr2 + πrs.

Practice Using the Formula for Different Size Cones

Now let's look at two examples. In the first example let's assume that you're given r = 2 and s = 5. If you plug these two numbers in, you get A = π(2)2 + π(2)(5), which is equal to 4 π + 10 π, which is equal to 14 π. So now let's look at a second example, but let's use some higher numbers this time. Let's assume that you're given r = 10 and s = 12. So plugging those numbers in you get A = π(10)2 + π(10)(12), which is equal to 100 π + 120 π, which is equal to 220 π. Here are two final notes for finding the surface area of a cone. The first that it is fine to leave your answer in pi, since that would be in the most precise terms. The second is that you can still find the answer if you're not given s and r but you're given the height. You would just need to use Pythagoras' Theorem.

Thank you for watching and for more information, visit About.com.

Find the Parts of a Cone

So first let's look at a diagram of a cone. We have a side length, which we're going to call S, which is the diagonal of the cone. We also have a base which is the circle at the bottom. On the circle we have labeled R, which is your radius. And your radius is just a line from one side of the circle to the center of the circle. In this diagram, we also have labeled h, which is the height of your cone. And you may or may not need to use the height in some problems.

Learn the Formula for Surface Area of a Cone

We're going to break the surface area formula into two parts. The first part is the area of the base, which as we said before, is the circle at the bottom of the cone. And the area of a circle is πr2. The second part of the surface area formula is the area of the actual conical section. And the area of a cone is πrs, where s is the side length and r is the radius. So to get the total area, we simply add the area of the base to the area of the conical section. So we have A = πr2 + πrs.

Practice Using the Formula for Different Size Cones

Now let's look at two examples. In the first example let's assume that you're given r = 2 and s = 5. If you plug these two numbers in, you get A = π(2)2 + π(2)(5), which is equal to 4 π + 10 π, which is equal to 14 π. So now let's look at a second example, but let's use some higher numbers this time. Let's assume that you're given r = 10 and s = 12. So plugging those numbers in you get A = π(10)2 + π(10)(12), which is equal to 100 π + 120 π, which is equal to 220 π. Here are two final notes for finding the surface area of a cone. The first that it is fine to leave your answer in pi, since that would be in the most precise terms. The second is that you can still find the answer if you're not given s and r but you're given the height. You would just need to use Pythagoras' Theorem.

Thank you for watching and for more information, visit About.com.

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