We are trying to fine (a) the height of a cone with a diameter of 18 and a slant height 15. If c= 15 what is (b)? Hint: we only need half of the diameter.

Answer 1

To find the height of the cone, we can use the Pythagorean theorem. In a right triangle formed by the radius, the height, and the slant height of the cone, the slant height is the hypotenuse, and the radius and height are the other two sides.

Given:

• Diameter of the cone = 18
• Radius (r) = Diameter / 2 = 18 / 2 = 9
• Slant height (c) = 15

Let's denote:

• Height of the cone = h

According to the Pythagorean theorem: \[ c^2 = r^2 + h^2 \]

Substituting the known values: \[ 15^2 = 9^2 + h^2 \] \[ 225 = 81 + h^2 \]

Now, solve for \( h^2 \): \[ h^2 = 225 - 81 \] \[ h^2 = 144 \]

Taking the square root of both sides: \[ h = \sqrt{144} = 12 \]

So, the height of the cone is 12.

To summarize: (a) The height of the cone is 12.

If you have any further questions or if (b) refers to something else, please let me know!

Answer 2

These are the answer options:

Option A: b = twice the diameter
Option B: b = 18
Option C: b = 9 (half the diameter)

Answer 3

Based on your hint, it seems that (b) refers to the radius of the cone, which is half of the diameter.

Given that the diameter of the cone is 18, the radius (which is half the diameter) would be:

\[ b = \frac{18}{2} = 9 \]

Thus, the correct option is:

Option C: b = 9 (half the diameter).

If you have any further questions or need additional assistance, feel free to ask!