The formula for the volume of a cone is:
V = (1/3)πr^2h
Where V is the volume, r is the radius of the base, h is the altitude (height) of the cone, and π is approximately 3.14159.
We can rearrange this formula to solve for the radius:
r = sqrt((3V)/(πh))
Plugging in the given values, we get:
r = sqrt((3 x 301.44)/(π x 8)) = 6 mm
Now, we can use the Pythagorean theorem to find the slant height of the cone:
l = sqrt(r^2 + h^2)
Plugging in the values we have, we get:
l = sqrt(6^2 + 8^2) = sqrt(100) = 10 mm
Therefore, the slant height of the cone is 10 mm.