How do you find the slant height of a cone whose height is 8 feet and whose diameter is 16 feet.

Study this diagram and use the Pythagorean theorem.

Remember that the radius of this circle's base is 8 feet.

http://3dshapes.org/3d-shapes-cone-shape.html

Ms Sue could you give me a little more help I've never done this kind of problem.

Did you look at that diagram?

Pythagorean Theorem:
a = length of base
b = height
c = slant height (hypotenuse)

a^2 + b^2 = c^2
8^2 + 8^2 = c^2
64 + 64 = c^2
128 = c^2
11.31 = c

To find the slant height of a cone, you can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by the height and radius of the cone.

1. Start by finding the radius of the cone. Since the diameter is given as 16 feet, divide it by 2 to get the radius: 16 feet ÷ 2 = 8 feet.

2. Now, draw a right triangle using the height, radius, and slant height of the cone. The height is given as 8 feet, and the radius we just found is also 8 feet.

3. Apply the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the slant height is the hypotenuse, the height is one side, and the radius is the other side.

Using the formula: slant height^2 = height^2 + radius^2
Substituting the given values: slant height^2 = 8^2 + 8^2

Simplifying: slant height^2 = 64 + 64 = 128

4. Take the square root of both sides to solve for the slant height: slant height = √128.

5. Simplify the square root: slant height ≈ 11.31 feet.

Therefore, the slant height of the cone is approximately 11.31 feet.