A solid is formed by a cone standing on a hemisphere. If the radius of the hemisphere is 1 cm and the height of the cone is equal to its radius, find the total volume of the solid.

The solid consists of a cone standing on a hemisphere.
The radius of the hemisphere ($r$) is $1 \text{ cm}$.
The radius of the cone ($r$) is equal to the radius of the hemisphere, so $r = 1 \text{ cm}$.
The height of the cone ($h$) is equal to its radius, so $h = 1 \text{ cm}$.

The formula for the volume of a cone is $V_{\text{cone}} = \frac{1}{3} \pi r^2 h$.
Substitute the values $r = 1 \text{ cm}$ and $h = 1 \text{ cm}$:

The formula for the volume of a hemisphere is $V_{\text{hemisphere}} = \frac{2}{3} \pi r^3$.
Substitute the value $r = 1 \text{ cm}$:

The total volume of the solid is the sum of the volume of the cone and the volume of the hemisphere.

The volume of the solid in terms of $\pi$ is $\boxed{\pi \text{ cm}^3}$.