Question: User: please do this same problem but with the formula $V = \pi r^2 h$
1. **Stating the problem:**
We need to find the volume $V$ of a cylinder using the formula $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height.
2. **Formula and explanation:**
The volume of a cylinder is calculated by multiplying the area of the circular base by the height. The area of the base is $\pi r^2$.
3. **Important rules:**
- $\pi$ is approximately 3.14159.
- Square the radius $r$ before multiplying by $\pi$ and $h$.
4. **Intermediate work:**
Suppose the radius $r = 3$ and height $h = 5$ (example values).
Calculate $r^2$:
$$r^2 = 3^2 = 9$$
Calculate volume:
$$V = \pi \times 9 \times 5$$
5. **Simplify:**
$$V = 45\pi$$
6. **Final answer:**
The volume of the cylinder is $$V = 45\pi$$ cubic units.
This means the volume depends on the radius squared times the height, multiplied by $\pi$.