What is the slant height of a cone with a radius of 7 and a altitude of 19?

If you visualize the cone by cutting it vertically (with a plane perpendicular to the base), you can construct a right triangle to represent the radius, altitude, and slant height. This triangle has legs of 7 (the radius) and 19 (the altitude). Its hypotenuse represents the slant height. We can then use the Pythagorean theorem to solve for the slant height:

72 + 192 = s2

72 + 192 = s2

410 = s2

s = √(410)

s ≈ 20.24

Therefore the cone has a slant height of √(410), or approximately 20.248456731316586933246902289901 units.