The perimeter of the base of a right circular cylinder is 44 cm and its height is 8 cm. Then, volume of the cylinder is : (Take $\pi=\frac{22}{7})$

Question

Accepted Answer

To determine the volume of the right circular cylinder, we need to use the formula for the volume of a cylinder, which is:

$$ V = \pi r^2 h $$

where $ V $ is the volume, $ r $ is the radius of the base, and $ h $ is the height of the cylinder.

Given:
- The perimeter (circumference) of the base of the cylinder is 44 cm.
- The height $ h $ of the cylinder is 8 cm.
- $\pi = \frac{22}{7}$.

First, we find the radius $ r $ of the base using the formula for the circumference of a circle:

$$ C = 2\pi r $$

Substituting the given perimeter:

$$ 44 = 2 \times \frac{22}{7} \times r $$

Solving for $ r $:

$$ 44 = \frac{44}{7} \times r $$

$$ r = \frac{44 \times 7}{44} $$

$$ r = 7 \text{ cm} $$

Now, we can calculate the volume of the cylinder:

$$ V = \pi r^2 h $$

$$ V = \frac{22}{7} \times 7^2 \times 8 $$

$$ V = \frac{22}{7} \times 49 \times 8 $$

$$ V = \frac{22 \times 392}{7} $$

$$ V = \frac{8624}{7} $$

$$ V = 1232 \text{ cm}^3 $$

Therefore, the volume of the cylinder is 1232 cm³, which corresponds to Option 2.

### Explanation for Other Options:

1. **Option 1 (1212 cm³):** This option is incorrect because the calculated volume using the given dimensions and formula does not result in 1212 cm³. The correct calculation yields 1232 cm³.

2. **Option 3 (1412 cm³):** This option is incorrect because it exceeds the calculated volume. The correct calculation, as shown, results in 1232 cm³, not 1412 cm³.

3. **Option 4 (1432 cm³):** This option is incorrect because it also exceeds the calculated volume. The correct calculation results in 1232 cm³, not 1432 cm³.

In conclusion, the correct answer is Option 2 (1232 cm³), as it accurately reflects the volume of the cylinder based on the given dimensions and the formula used.