How Do You Find the Slant Height of a Cone?

The slant height is the distance from the tip of the cone to a point on the edge of the base
'r' stands for the radius of the base
'h' stands for the height of the cone
'a' and 'b' represent the legs of the right triangle
'c' represents the hypotenuse of the right triangle
'h' and 'r' are the legs of our right triangle, so they can replace 'a' and 'b'
'l' is the hypotenuse of our right triangle, so it can replace 'c'

1. The radius is the distance from the center of the base to its outer edge
2. The height is the distance from the center of the base to the tip of the cone
3. The slant height is the distance from the tip of the cone to a point on the edge of the base
1. The Pythagorean Theorem allows us to find a missing side of a right triangle if we know the two other sides
1. 'a' and 'b' represent the legs of the right triangle
2. 'c' represents the hypotenuse, or longest side, of the right triangle
3. We can replace 'a' and 'b' in the Pythagorean Theorem with 'h' and 'r' - the two legs of our triangle
4. We can replace 'c' in the Pythagorean Theorem with 'l' - the hypotenuse of our triangle
1. The height is the distance from the center of the base to the tip of the cone
2. The radius is the distance from the center of the base to its outer edge
3. The slant height is the distance from the tip of the cone to a point on the edge of the base
1. Plug 15 in for 'h' and 8 in for 'r' into h² + r² = l² to find 'l'
1. First square the numbers on the left: 15² = 225 and 8² = 64
2. Adding 225+64 gives us 289 on the left
3. Take the square root of both sides to get rid of the square
4. The square root of 289 is 17

Find the slant height of the cone below: