A cylinder and a cone are of same base radius and of same height. Find the ratio of the volumes of cylinder to that of the cone.

Answer

To find the ratio of the volumes of a cylinder to that of a cone, both having the same base radius and height, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the formulas for the volumes**:
- The volume \( V \) of a cylinder is given by the formula:
\[ V_{\text{cylinder}} = \pi r^2 h \]
- The volume \( V \) of a cone is given by the formula:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]

2. **Set up the ratio of the volumes**:
- We need to find the ratio of the volume of the cylinder to the volume of the cone:
\[ \text{Ratio} = \frac{V_{\text{cylinder}}}{V_{\text{cone}}} \]

3. **Substitute the volume formulas into the ratio**:
- Substitute the formulas we identified:
\[ \text{Ratio} = \frac{\pi r^2 h}{\frac{1}{3} \pi r^2 h} \]

4. **Simplify the ratio**:
- The common terms \( \pi r^2 h \) in the numerator and denominator cancel out:
\[ \text{Ratio} = \frac{1}{\frac{1}{3}} = 3 \]

5. **Express the ratio in standard form**:
- The ratio of the volumes can be expressed as:
\[ \text{Ratio} = 3 : 1 \]

### Final Answer:
The ratio of the volumes of the cylinder to that of the cone is \( 3 : 1 \).

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