Introduction to Geometry 63 Surface Area of a Right Circular Cone

Our last lesson for intro to geometry is going to focus on the surface area of right circular cone. So right circular cone is is three-dimensional object with circular base just one base circular base right here. And the reason it's right circular cone is because when we draw line from the top of the cone to the middle of the or the center should say of the circle. It's going to be perpendicular and it's going to form right triangle with the radius of the cone and the side of the cone. So to find the surface area of right circular cone, we have to take the area of the bottom plus the area of the sides. So the area of the bottom is the area of normal circle. So r^ 2. Now the area of the cone part is pi rs. So we take which is the slant height of the cone which is this which is this height right here. Normally we are going to use perpendicular height but for this we don't use the perpendicular height. We're going to use what's called the slant height and of course is the radius. So this part is how we find the area of the cone shaped part. So now that we know how to find the surface area, we're going to do couple examples. So, first example, we have this cone right here. And so that we make sure that we're plugging in all the right numbers, we're going to write little list over here. So, equals and equals or our radius equals 3 because if you look, this is the center of the circle. This line right here is drawn to point on the circle. So that's our radius. So equals 3. And our height, should have wrote wrote by accident. So which is our slant height, is this height right here, the hypotenuse of this right triangle that's formed when you drop altitude down. So our equals 5. So to find the surface area, we're going to use our formula, which is pi * * our slant height + r^ 2. So our slant height or surface area is equal to pi 3 * 5 + 3 squared. So 3 * 5 is 15 15i + 3^ 2ar is 9 9 pi. So our surface area is equal to 15 + 9 which is 24 pi and we're going to leave it just like that so that we are giving the exact value but we can't forget our units. So our units are inches squared because area is always measured in units squared. So we're going to do one more example. So equ= equals. So our right here is unknown. So to solve for our we're going to use our pythagorean theorem which says that squar which is 2 + 2 = c^2. So 2 + 8^2 which is 64 is equal to 10^2 which is 100. If you minus the 64 over you get r^2 is equal to 36. You take the square root you get is equal to 6. Now you remember when we take the square root we always get positive or negative square root. But since we're talking about the length of something we can't have negative length. So we only take the positive value. So our is six, our is 10. And now we can find our surface area. So surface area is equal to + 2. Now, you don't have to write the formula every time you solve the problem, but when we're just starting to learn, it helps to write it out so you can memorize it because these are all things you'll need to have memorized. So, pi which is 6 * which is 10, plus pi squared. So surface area is equal to 6 * 10 which is 60. 60 60 + 6 * 6^ 2ar is 36. So 36 pi. So our final answer is 96i cm squared. So, like said, this is our last lesson for intro to geometry, but we're going to start our geometry series soon. So, make sure you come back and check that out.