The volume of a right circular cylinder can be obtained from its curved surface area by multiplying it by its

Options

A. `("radius")/(2)`
B. `(2)/("radius")`
C. height
D. 2 `xx` height

Answer

To find the volume of a right circular cylinder from its curved surface area, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formulas**:
- The formula for the **curved surface area (CSA)** of a right circular cylinder is given by:
\[ \text{CSA} = 2 \pi r h \]
- The formula for the **volume (V)** of a right circular cylinder is given by:
\[ V = \pi r^2 h \]

2. **Relate the volume to the curved surface area**:
- We want to express the volume in terms of the curved surface area. From the CSA formula, we can isolate \(h\):
\[ h = \frac{\text{CSA}}{2 \pi r} \]

3. **Substitute \(h\) into the volume formula**:
- Now, substitute \(h\) back into the volume formula:
\[ V = \pi r^2 \left(\frac{\text{CSA}}{2 \pi r}\right) \]

4. **Simplify the expression**:
- When we simplify this expression, we can cancel \(\pi\) and one \(r\):
\[ V = \frac{r \cdot \text{CSA}}{2} \]

5. **Conclusion**:
- Therefore, to find the volume of a right circular cylinder from its curved surface area, you multiply the curved surface area by the radius and then divide by 2:
\[ V = \frac{r \cdot \text{CSA}}{2} \]

### Final Answer:
The volume of a right circular cylinder can be obtained from its curved surface area by multiplying it by its radius divided by 2.

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