Answer:

Step-by-step explanation:
First, we know that the slant height is 10 cm and the diameter is 6 cm.
Since our diameter is 6 cm, our radius is just half of that. Namely:

To find the vertical height, we can use some geometry.
If we look closely, we can see that the vertical height, slant height, and the radius form a right triangle.
So, to find the vertical height, we can use the Pythagorean Theorem:

In this case, c, our hypotenuse, is our slant height.
So, let's substitute 3 for a, h for b, and 10 for c. This yields:

Square:

Subtract 9 from both sides:

Take the square root of both sides:

Approximate. Use a calculator. So:

And we're done!
Edit: Added Unit