Question

A 3-D modeler is designing a component of a castle in a video game. She places a cone on top of a cylinder, so they lineup and share the same radius. The cone and the cylinder share the same height. If the volume of the cone is 50 cm what is the volume of the whole object?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the volume of the whole object, we need to add the volume of the cone and the cylinder together.

The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.

Since the cone and the cylinder share the same height, we can use the same h for both the cone and cylinder.

Given that the volume of the cone is 50 cm^3, we can set up the equation:

50 = (1/3)πr^2h

Solving for r^2, we get:

r^2 = 150/(πh)

Since the cone and the cylinder share the same radius, we can find the volume of the cylinder using the formula V = πr^2h:

V_cylinder = πr^2h = π(150/(πh))h = 150 cm^3

Therefore, the volume of the whole object (cone and cylinder combined) is:

V_total = V_cone + V_cylinder = 50 + 150 = 200 cm^3

Thus, the volume of the whole object is 200 cm^3.