A 3D modeler is designing a component of a castle in a video game. She places a cone on top of a cylinder so they line up and share the same radius. The cone and the cylinder share the same height. If the volume of the cone is 50 cm3 , what is the volume of the whole object?
(1 point)
The volume of the cone can be given by the formula V = 1/3 * π * r^2 * h, where V is the volume, π is a constant (approximately 3.14159), r is the radius, and h is the height.
Since the cone and the cylinder share the same height and radius, the volume of the cylinder can also be given by the formula V = π * r^2 * h.
Given that the volume of the cone is 50 cm3, we can equate the two formulas and solve for the volume of the whole object.
1/3 * π * r^2 * h = 50
Multiplying both sides by 3/π gives:
r^2 * h = (50 * 3) / π = 150 / π
The volume of the whole object can then be given by the sum of the volume of the cone and the cylinder:
V_total = V_cone + V_cylinder = 1/3 * π * r^2 * h + π * r^2 * h
= (1/3 + 1) * π * r^2 * h
= 4/3 * π * r^2 * h
Substituting the value of the volume of the cone we found earlier:
V_total = 4/3 * π * r^2 * h
= 4/3 * π * (150 / π) * h
= 4 * 150 * h / 3
= 600 * h / 3
= 200 * h
Therefore, the volume of the whole object is 200 * h cm3.