Question

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?

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's denote the height and radius of the cone and cylinder as h and r, respectively.

The volume of a cone is given by the formula V = (1/3)πr^2h.
Since the volume of the cone is given as 50 cm³, we have 50 = (1/3)πr^2h.

The volume of a cylinder is given by the formula V = πr^2h.

Since the cone and cylinder share the same height, h is the same for both shapes.

Substitute the given volume of the cone into the equation for the volume of the cone:
50 = (1/3)πr^2h.

Now, solve for h in terms of r:
h = 150 / πr^2.

Now, we can calculate the volume of the whole object, which is the sum of the volumes of the cone and cylinder:
V_total = V_cone + V_cylinder
= 50 + πr^2 * (150 / πr^2)
= 50 + 150
= 200 cm³.

Therefore, the volume of the whole object is 200 cm³.