Volume of a right circular cylinder of height 21 cm and base radius 5 cm is :

Options

A. `1255 cm^(3)`
B. `1050 cm^(3)`
C. `1175 cm^(3)`
D. `1650 cm^(3)`

Answer

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

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

where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder,
- \( \pi \) is a constant approximately equal to \( \frac{22}{7} \) or \( 3.14 \).

### Step-by-Step Solution:

1. **Identify the given values:**
- Height (\( h \)) = 21 cm
- Radius (\( r \)) = 5 cm

2. **Substitute the values into the volume formula:**
\[ \text{Volume} = \pi \times (5 \, \text{cm})^2 \times (21 \, \text{cm}) \]

3. **Calculate \( r^2 \):**
\[ (5 \, \text{cm})^2 = 25 \, \text{cm}^2 \]

4. **Substitute \( r^2 \) back into the volume formula:**
\[ \text{Volume} = \pi \times 25 \, \text{cm}^2 \times 21 \, \text{cm} \]

5. **Multiply the constants:**
\[ 25 \times 21 = 525 \, \text{cm}^3 \]

6. **Now, substitute \( \pi \) with \( \frac{22}{7} \):**
\[ \text{Volume} = \frac{22}{7} \times 525 \, \text{cm}^3 \]

7. **Calculate the multiplication:**
\[ \frac{22 \times 525}{7} = \frac{11550}{7} = 1650 \, \text{cm}^3 \]

8. **Final answer:**
\[ \text{Volume} = 1650 \, \text{cm}^3 \]

### Conclusion:
The volume of the right circular cylinder is \( 1650 \, \text{cm}^3 \).

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