The diamter of a closed cylinder is 7 cm and its heght is 16 cm. Find:
the volume of the cylinder .[Take `pi =22/(7)]`

Answer

To find the volume of a closed cylinder, we can follow these steps:

### Step 1: Identify the given values
- Diameter of the cylinder (d) = 7 cm
- Height of the cylinder (h) = 16 cm

### Step 2: Calculate the radius
The radius (r) of the cylinder can be calculated using the formula:
\[ r = \frac{d}{2} \]
Substituting the value of the diameter:
\[ r = \frac{7 \, \text{cm}}{2} = 3.5 \, \text{cm} \]

### Step 3: Write the formula for the volume of a cylinder
The formula for the volume (V) of a cylinder is:
\[ V = \pi r^2 h \]

### Step 4: Substitute the values into the formula
Using the value of \(\pi = \frac{22}{7}\), the radius \(r = 3.5 \, \text{cm}\), and height \(h = 16 \, \text{cm}\):
\[ V = \frac{22}{7} \times (3.5)^2 \times 16 \]

### Step 5: Calculate \(r^2\)
First, calculate \(r^2\):
\[ (3.5)^2 = 12.25 \]

### Step 6: Substitute \(r^2\) back into the volume formula
Now substituting \(r^2\) back into the volume formula:
\[ V = \frac{22}{7} \times 12.25 \times 16 \]

### Step 7: Simplify the calculation
1. Calculate \(12.25 \times 16\):
\[ 12.25 \times 16 = 196 \]

2. Now substitute this back into the volume formula:
\[ V = \frac{22}{7} \times 196 \]

### Step 8: Perform the multiplication
To simplify:
\[ V = \frac{22 \times 196}{7} \]
Calculating \(22 \times 196\):
\[ 22 \times 196 = 4312 \]
Now divide by 7:
\[ V = \frac{4312}{7} = 616 \]

### Step 9: State the final answer
Thus, the volume of the cylinder is:
\[ V = 616 \, \text{cm}^3 \]