State True or False:
A solid cylinder of radius r and height h is placed over other cylinder of same height and radius. The total surface area of the shape so formed is `4pi h + 4pi r^2`

Answer

To determine whether the statement is true or false, we need to calculate the total surface area of the combined shape formed by stacking two identical cylinders on top of each other.

### Step-by-Step Solution:

1. **Identify the dimensions of the cylinders**:
- Each cylinder has a radius \( r \) and height \( h \).

2. **Determine the height of the combined shape**:
- When one cylinder is placed on top of another, the total height becomes \( h + h = 2h \).

3. **Calculate the total surface area**:
- The total surface area (TSA) of a cylinder is given by the formula:
\[ \text{TSA} = 2\pi r h + 2\pi r^2 \]
where \( 2\pi r h \) is the curved surface area and \( 2\pi r^2 \) accounts for the area of the two circular bases.

4. **Substituting the height in the formula**:
- For the combined cylinder, the height is \( 2h \), so we substitute \( h \) with \( 2h \):
\[ \text{TSA} = 2\pi r (2h) + 2\pi r^2 = 4\pi rh + 2\pi r^2 \]

5. **Compare with the given statement**:
- The statement claims that the total surface area is \( 4\pi h + 4\pi r^2 \).
- Our calculation shows that the total surface area is \( 4\pi rh + 2\pi r^2 \).

6. **Conclusion**:
- Since \( 4\pi rh + 2\pi r^2 \) is not equal to \( 4\pi h + 4\pi r^2 \), the statement is **False**.

### Final Answer:
**False**