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

Options

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

Answer

To find the height of the cylinder given its volume and curved surface area, we can follow these steps:

### Step 1: Write down the formulas
The volume \( V \) of a cylinder is given by the formula:
\[ V = \pi r^2 h \]
The curved surface area \( A \) of a cylinder is given by the formula:
\[ A = 2 \pi r h \]

### Step 2: Substitute the known values
From the problem, we know:
- Volume \( V = 924 \, m^3 \)
- Curved Surface Area \( A = 264 \, m^2 \)

We can set up the equations:
1. \( \pi r^2 h = 924 \) (Equation 1)
2. \( 2 \pi r h = 264 \) (Equation 2)

### Step 3: Simplify Equation 2
From Equation 2, we can express \( h \) in terms of \( r \):
\[ h = \frac{264}{2 \pi r} \]
Substituting \( \pi \) as \( \frac{22}{7} \):
\[ h = \frac{264}{2 \times \frac{22}{7} \times r} = \frac{264 \times 7}{44r} = \frac{42}{r} \]

### Step 4: Substitute \( h \) in Equation 1
Now substitute \( h \) in Equation 1:
\[ \pi r^2 \left(\frac{42}{r}\right) = 924 \]
This simplifies to:
\[ 42 \pi r = 924 \]
Dividing both sides by \( \pi \):
\[ r = \frac{924}{42 \pi} \]
Substituting \( \pi \) as \( \frac{22}{7} \):
\[ r = \frac{924 \times 7}{42 \times 22} \]
Calculating:
\[ r = \frac{6488}{924} = 7 \, m \]

### Step 5: Find the height \( h \)
Now that we have \( r \), we can find \( h \):
\[ h = \frac{42}{r} = \frac{42}{7} = 6 \, m \]

### Conclusion
The height of the cylinder is \( 6 \, m \).

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