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, we will follow these steps:

### Step 1: Identify the dimensions
Given:
- Radius of the cone (r) = 1 cm
- Height of the cone (h) = 1 cm (since the height of the cone is equal to its radius)
- Radius of the hemisphere = 1 cm

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

### Step 3: Calculate the volume of the hemisphere
The formula for the volume of a hemisphere is:
\[ V_{hemisphere} = \frac{2}{3} \pi r^3 \]
Substituting the value of the radius:
\[ V_{hemisphere} = \frac{2}{3} \pi (1)^3 = \frac{2}{3} \pi \cdot 1 = \frac{2}{3} \pi \]

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

### Step 5: State the final answer
The volume of the solid in terms of \(\pi\) is:
\[ \text{Volume} = \pi \text{ cm}^3 \]