To find the volume of the whole object (the cone and the cylinder), we need to calculate the volume of the cylinder and then add it to the volume of the cone.
The volume \( V \) of a cone is given by the formula:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius of the base and \( h \) is the height.
The volume \( V \) of a cylinder is given by the formula:
\[ V_{\text{cylinder}} = \pi r^2 h \]
In this case, we know the volume of the cone is \( 50 , \text{cm}^3 \). Setting the volume of the cone equal to the formula:
\[ 50 = \frac{1}{3} \pi r^2 h \]
From this, we can express \( \pi r^2 h \):
\[ \pi r^2 h = 150 , \text{cm}^3 \]
Now, to find the volume of the cylinder:
\[ V_{\text{cylinder}} = \pi r^2 h = 150 , \text{cm}^3 \]
Now we can find the total volume of the whole object:
\[ V_{\text{total}} = V_{\text{cone}} + V_{\text{cylinder}} = 50 , \text{cm}^3 + 150 , \text{cm}^3 = 200 , \text{cm}^3 \]
Thus, the total volume of the whole object is:
\[ \boxed{200} , \text{cm}^3 \]