The formula for the volume of a cone is:
V = (1/3)πr²h
where r is the radius of the base, h is the height of the cone, and π is pi.
In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:
h² = s² - r²
h² = 17² - 8²
h² = 225
h = 15
Now that we have the height, we can plug in the values for r and h into the formula for the volume:
V = (1/3)π(8²)(15)
V = (1/3)π(64)(15)
V = (1/3)(960π)
V = 320π
Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.