To find the volume of the whole object, we need to calculate the volumes of both the cylinder and the cone, and then combine them.
The formula for the volume of a cone is: \[ V_{cone} = \frac{1}{3} \pi r^2 h \]
The formula for the volume of a cylinder is: \[ V_{cylinder} = \pi r^2 h \]
From the problem, we know the following:
- The volume of the cone (\( V_{cone} \)) is 50 cm³.
- Both the cone and the cylinder share the same radius (r) and height (h).
Since the volumes use the same radius and height, we can determine the volume of the cylinder by rearranging the cone's volume formula.
Given the cone's volume formula: \[ 50 = \frac{1}{3} \pi r^2 h \]
We can find \( r^2 h \): \[ r^2 h = 50 \cdot 3 / \pi = \frac{150}{\pi} \]
Now, we can find the volume of the cylinder: \[ V_{cylinder} = \pi r^2 h = \pi \left(\frac{150}{\pi}\right) = 150 \text{ cm}^3 \]
Now, to find the total volume of the whole object (the cone and the cylinder combined): \[ V_{total} = V_{cone} + V_{cylinder} \] \[ V_{total} = 50 + 150 = 200 \text{ cm}^3 \]
Thus, the volume of the whole object is 200 cm³.