A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of `pi`

Explanation

To find the volume of the solid that consists of a cone standing on a hemisphere, both with a radius of 1 cm and the height of the cone also being 1 cm, we can follow these steps:

### Step 1: Identify the dimensions
- The radius \( r \) of both the cone and the hemisphere is given as \( 1 \, \text{cm} \).
- The height \( h \) of the cone is also given as \( 1 \, \text{cm} \).

### Step 2: Calculate the volume of the cone
The formula for the volume \( V \) of a cone is given by:
\[ V = \frac{1}{3} \pi r^2 h \]
Substituting the values of \( r \) and \( h \):
\[ V_{\text{cone}} = \frac{1}{3} \pi (1)^2 (1) = \frac{1}{3} \pi \, \text{cm}^3 \]

### Step 3: Calculate the volume of the hemisphere
The formula for the volume \( V \) of a hemisphere is given by:
\[ V = \frac{2}{3} \pi r^3 \]
Substituting the value of \( r \):
\[ V_{\text{hemisphere}} = \frac{2}{3} \pi (1)^3 = \frac{2}{3} \pi \, \text{cm}^3 \]

### Step 4: Find the total volume of the solid
The total volume of the solid is the sum of the volumes of the cone and the hemisphere:
\[ V_{\text{total}} = V_{\text{cone}} + V_{\text{hemisphere}} \]
Substituting the volumes we calculated:
\[ V_{\text{total}} = \frac{1}{3} \pi + \frac{2}{3} \pi = \frac{3}{3} \pi = \pi \, \text{cm}^3 \]

### Final Answer
The volume of the solid is:
\[ \boxed{\pi \, \text{cm}^3} \]