The curved surface area of a cylindrical pillar is 264 `m^2` and its volume is 924 `m^3` . The height of the pillar is

Options

A. 4 m
B. 5 m
C. 6 m
D. 7 m

Explanation

To find the height of the cylindrical pillar given its curved surface area and volume, we can use the formulas for the curved surface area (CSA) and volume of a cylinder.

### Step-by-Step Solution:

1. **Identify the formulas:**
The formulas for the curved surface area (CSA) and volume (V) of a cylinder are:
- Curved Surface Area (CSA) = \( 2 \pi r h \)
- Volume (V) = \( \pi r^2 h \)

2. **Given values:**
- Curved Surface Area (CSA) = 264 m²
- Volume (V) = 924 m³

3. **Set up the equations:**
From the CSA formula:
\[ 2 \pi r h = 264 \quad \text{(1)} \]
From the Volume formula:
\[ \pi r^2 h = 924 \quad \text{(2)} \]

4. **Express \( h \) from equation (1):**
Rearranging equation (1) for \( h \):
\[ h = \frac{264}{2 \pi r} = \frac{132}{\pi r} \quad \text{(3)} \]

5. **Substitute \( h \) in equation (2):**
Substitute equation (3) into equation (2):
\[ \pi r^2 \left(\frac{132}{\pi r}\right) = 924 \]
Simplifying this gives:
\[ 132 r = 924 \]

6. **Solve for \( r \):**
\[ r = \frac{924}{132} = 7 \quad \text{(4)} \]

7. **Substitute \( r \) back to find \( h \):**
Now substitute \( r = 7 \) back into equation (3) to find \( h \):
\[ h = \frac{132}{\pi \times 7} \]
Using \( \pi \approx \frac{22}{7} \):
\[ h = \frac{132}{\frac{22}{7} \times 7} = \frac{132}{22} = 6 \]

8. **Final answer:**
The height of the pillar is \( h = 6 \, m \).