The radius of the base and the height of a cylinder are `14 cm` and `20 cm` , respectively .What is the volume of the cylinder ?

Options

A. `12380 cm^(3)`
B. `12350 cm^(3)`
C. `13220 cm^(3)`
D. `12320 cm^(3)`

Answer

To find the volume of a cylinder, we can use the formula:

\[ \text{Volume} = \pi r^2 h \]

where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is a constant approximately equal to \( \frac{22}{7} \).

### Step-by-step solution:

1. **Identify the given values:**
- Radius \( r = 14 \, \text{cm} \)
- Height \( h = 20 \, \text{cm} \)

2. **Substitute the values into the volume formula:**
\[ \text{Volume} = \pi r^2 h = \frac{22}{7} \times (14)^2 \times 20 \]

3. **Calculate \( r^2 \):**
\[ (14)^2 = 14 \times 14 = 196 \]

4. **Substitute \( r^2 \) back into the volume formula:**
\[ \text{Volume} = \frac{22}{7} \times 196 \times 20 \]

5. **Multiply \( 196 \) by \( 20 \):**
\[ 196 \times 20 = 3920 \]

6. **Now substitute this value back into the volume formula:**
\[ \text{Volume} = \frac{22}{7} \times 3920 \]

7. **Multiply \( 3920 \) by \( 22 \):**
\[ 3920 \times 22 = 86240 \]

8. **Now divide by \( 7 \):**
\[ \text{Volume} = \frac{86240}{7} = 12320 \, \text{cm}^3 \]

### Final Answer:
The volume of the cylinder is \( 12320 \, \text{cm}^3 \).

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