Question

A cone is stacked on top of a cylinder. They both share a circular base. The total height of the composite figure is 25. The height of the cylinder is 13 and the radius is 5.
Which expression represents the volume, in cubic units, of the composite figure?

Pi(52)(13) – One-third pi (52)(12)
Pi(52)(13) – One-third pi (52)(25)
Pi(52)(13) + One-third pi (52)(12)
Pi(52)(13) + One-third pi (52)(25)

Answer 1

Cylinder volume = π(5^2)(13). Cone height = 25 − 13 = 12, so cone volume = (1/3)π(5^2)(12). Thus the correct expression is

Pi(5^2)(13) + One-third pi (5^2)(12),

which simplifies to 425π cubic units.