A solid oblique cone with a slant length of 17 units is placed inside an empty cylinder with a congruent base of radius 8 units and a height of 15 units.

What is the unfilled volume inside the cylinder?

320π cubic units

597π cubic units

640π cubic units

725π cubic units

Solving for the volume of an oblique cone is the same as solving for the volume of a right circular cone.

V = π r² h/3

Since the slant length is given, we need to solve for the height. In a right triangle the slant length is the hypotenuse and the given radius serves as the short leg. We use the Pythagorean theorem to solve for the height.

a² + b² = c²

a² + 8² = 17²

a² = 17² - 8² = 289 - 64

a² = 225

a = √225 = 15

Volume of oblique cone = π * 8² * 15/3 = π * 64 * 5 = 320π cubic units

Volume of cylinder = π r² h = π * 8² * 15 = π * 64 * 15 = 960π cubic units

Volume of unfilled portion of the cylinder:

960π cubic units - 320π cubic units = 640π cubic units. Choice C.