The area of the curved surface of a right circular cylinder is `17.5m^(2)` and its volume is `14m^(3)`. What is the radius of is base?

Options

A. 0.8m
B. 2m
C. 1.6m
D. 2.5m

Answer

To find the radius of the base of a right circular cylinder given the curved surface area and volume, we can follow these steps:

### Step-by-Step Solution:

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

2. **Set up the equations:**
- From the problem, we know:
\[ 2\pi rh = 17.5 \quad \text{(1)} \]
\[ \pi r^2 h = 14 \quad \text{(2)} \]

3. **Express \(h\) in terms of \(r\) from equation (1):**
- Rearranging equation (1) gives:
\[ rh = \frac{17.5}{2\pi} \]
- Thus, we can express \(h\) as:
\[ h = \frac{17.5}{2\pi r} \quad \text{(3)} \]

4. **Substitute \(h\) from equation (3) into equation (2):**
- Substitute \(h\) in equation (2):
\[ \pi r^2 \left(\frac{17.5}{2\pi r}\right) = 14 \]
- Simplifying this gives:
\[ \frac{17.5 r}{2} = 14 \]

5. **Solve for \(r\):**
- Multiply both sides by 2:
\[ 17.5 r = 28 \]
- Now, divide both sides by 17.5:
\[ r = \frac{28}{17.5} \]
- Calculating this gives:
\[ r = 1.6 \text{ m} \]

### Final Answer:
The radius of the base of the cylinder is \(1.6 \, \text{m}\).