Assertion (A) : A solid is in the form 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. The volume of the solid is `pi` `cm^3`.
Reason (R) : Volume of cone `= (1)/(3) pi r^(2)h` and volume of hemi-sphere `= (2)/(3) pi r^(3)`

Options

A. Both A and R are true and R is the correct explanation of A.
B. Both A and R are true and R is not the correct explanation of A.
C. A is true but R is false
D. A is false but R is true

Answer

To solve the problem, we need to calculate the volume of the solid formed by a cone standing on a hemisphere, both having a radius of 1 cm and the height of the cone also being 1 cm. We will verify the assertion and reason provided in the question.

### Step-by-Step Solution:

1. **Identify the shapes and their dimensions**:
- The radius (r) of both the cone and the hemisphere is given as 1 cm.
- The height (h) of the cone is also given as 1 cm.

2. **Calculate the volume of the hemisphere**:
- The formula for the volume of a hemisphere is:
\[ V_{\text{hemisphere}} = \frac{2}{3} \pi r^3 \]
- Substituting \( r = 1 \):
\[ V_{\text{hemisphere}} = \frac{2}{3} \pi (1)^3 = \frac{2}{3} \pi \text{ cm}^3 \]

3. **Calculate the volume of the cone**:
- The formula for the volume of a cone is:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]
- Substituting \( r = 1 \) and \( h = 1 \):
\[ V_{\text{cone}} = \frac{1}{3} \pi (1)^2 (1) = \frac{1}{3} \pi \text{ cm}^3 \]

4. **Calculate the total volume of the solid**:
- The total volume of the solid is the sum of the volumes of the hemisphere and the cone:
\[ V_{\text{total}} = V_{\text{hemisphere}} + V_{\text{cone}} = \frac{2}{3} \pi + \frac{1}{3} \pi \]
- Finding a common denominator:
\[ V_{\text{total}} = \frac{2\pi + 1\pi}{3} = \frac{3\pi}{3} = \pi \text{ cm}^3 \]

5. **Conclusion**:
- The total volume of the solid is \( \pi \text{ cm}^3 \), which confirms the assertion (A) is true.
- The reason (R) provided is also correct as it states the formulas used for calculating the volumes of the cone and hemisphere.

### Final Answer:
Both assertion (A) and reason (R) are true, and R is the correct explanation of A.