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?

(1 point)
cm3

Asked on 2024-12-13 00:46:02

Answers

To find the total volume of the whole object (the cone and the cylinder), we first need to calculate the volume of the cylinder and then add the volume of the cone.

Given that the volume of the cone is \( V_{cone} = 50 \, \text{cm}^3 \).

The volume \( V \) of a cone is given by the formula:
\[
V_{cone} = \frac{1}{3} \pi r^2 h
\]
where \( r \) is the radius and \( h \) is the height. Since we know the volume of the cone, we denote its height as \( h \).

The volume \( V \) of a cylinder is given by the formula:
\[
V_{cylinder} = \pi r^2 h
\]

Since the cone and cylinder share the same radius \( r \) and height \( h \), we can express the volume of the cylinder as three times the volume of the cone:
\[
V_{cylinder} = 3 \times V_{cone} = 3 \times 50 \, \text{cm}^3 = 150 \, \text{cm}^3
\]

Now, we can calculate the total volume of the object:
\[
V_{total} = V_{cone} + V_{cylinder}
\]
\[
V_{total} = 50 \, \text{cm}^3 + 150 \, \text{cm}^3 = 200 \, \text{cm}^3
\]

Thus, the volume of the whole object is \( \boxed{200} \, \text{cm}^3 \).