The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm, how many liters of water can it hold ?

Question

Accepted Answer

To determine how many liters of water the cylindrical vessel can hold, we need to calculate the volume of the cylinder. The formula for the volume $ V $ of a cylinder is given by:

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

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

1. **Calculate the radius:**
   - The circumference $ C $ of the base is given as 132 cm. The formula for the circumference of a circle is:

$$ C = 2\pi r $$

Solving for $ r $:

$$ r = \frac{C}{2\pi} = \frac{132}{2\pi} = \frac{132}{2 \times 3.14} \approx \frac{132}{6.28} \approx 21 \text{ cm} $$

2. **Calculate the volume:**
   - Now that we have the radius, we can calculate the volume using the height $ h = 25 $ cm:

$$ V = \pi r^2 h = 3.14 \times 21^2 \times 25 $$

$$ V = 3.14 \times 441 \times 25 $$

$$ V = 3.14 \times 11025 $$

$$ V \approx 34696.5 \text{ cubic centimeters} $$

3. **Convert cubic centimeters to liters:**
   - Since 1 liter = 1000 cubic centimeters, we convert the volume to liters:

$$ \text{Volume in liters} = \frac{34696.5}{1000} \approx 34.6965 \text{ liters} $$

Rounding this to two decimal places gives approximately 34.70 liters. However, considering the options provided, the closest and most reasonable approximation is 34.65 liters.

Therefore, Option 2 (34.65 liters) is the correct answer.

**Explanation for Incorrect Options:**

- **Option 1 (33.64 liters):** This value is lower than the calculated volume of approximately 34.70 liters. It does not match the expected volume based on the given dimensions of the cylinder.

- **Option 3 (69.34 liters):** This value is significantly higher than the calculated volume. It is not consistent with the dimensions provided, as the calculated volume is approximately 34.70 liters.

- **Option 4 (22.35 liters):** This value is much lower than the calculated volume. It does not align with the expected volume of the cylinder, which is approximately 34.70 liters.

In conclusion, based on the calculations and the given options, Option 2 (34.65 liters) is the correct answer.