Question

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A 3-dimensional cone is placed on top of a 3-dimensional cylinder. One of the cylinder bases is common to the cone, with the same circumference.

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)
cm3

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. Given that the cone has a volume of 50 cm3, we can set up the equation:

50 = (1/3)πr^2h

Since the cone and the cylinder have the same height and radius, we can represent the radius as r and the height as h.

The volume of a cylinder is given by the formula V = πr^2h. Therefore, the volume of the cylinder in this case would be:

V_cylinder = πr^2h

To find the volume of the whole object, we add the volume of the cone and the cylinder:

V_whole object = V_cone + V_cylinder
= (1/3)πr^2h + πr^2h
= πr^2h((1/3) + 1)
= πr^2h(4/3)
= (4π/3) r^2h

Therefore, the volume of the whole object is (4π/3) r^2h. However, the specific value in cm³ cannot be determined without knowing the values of the radius and height that correspond to the cone and cylinder.