Question

A cylindrical bucket 28 cm in diameter and 72 cm height is full of water. The water is emptied into a rectangular vessel 66cm long and 28 cm wid Find the height of the water level in the tank.

• A. 20cm
• B. 30cm
• C. 24cm
• D. 35cm
• E. None of these

Answer 1

The Correct Option is C

Step 1: Understand the problem.
The water is emptied from a cylindrical bucket into a rectangular vessel. We need to find the height of the water level in the tank. Given values:
- Diameter of the cylindrical bucket = 28 cm
- Height of the cylindrical bucket = 72 cm
- Length of the rectangular vessel = 66 cm
- Width of the rectangular vessel = 28 cm

Step 2: Calculate the volume of water in the cylindrical bucket.
The volume \( V \) of a cylinder is given by the formula:
\( V = \pi r^2 h \)
where: - \( r \) is the radius of the cylinder, - \( h \) is the height of the cylinder.
The radius \( r = \frac{\text{diameter}}{2} = \frac{28}{2} = 14 \, \text{cm} \), and the height \( h = 72 \, \text{cm} \).
So, the volume of the water in the cylindrical bucket is:
\( V = \pi \times 14^2 \times 72 \)
\( V = \pi \times 196 \times 72 \)
\( V = \pi \times 14112 \)
\( V = 14112 \pi \, \text{cm}^3 \)

Step 3: Calculate the height of the water in the rectangular vessel.
The volume of water in the rectangular vessel will be the same as the volume of water in the cylindrical bucket. The volume \( V \) of a rectangular vessel is given by:
\( V = \text{length} \times \text{width} \times \text{height of water} \)
Let the height of the water in the vessel be \( h_{\text{vessel}} \). The volume of the rectangular vessel is:
\( 14112 \pi = 66 \times 28 \times h_{\text{vessel}} \)
\( 14112 \pi = 1848 \times h_{\text{vessel}} \)
Dividing both sides by 1848:
\( h_{\text{vessel}} = \frac{14112 \pi}{1848} \)
\( h_{\text{vessel}} = 24 \, \text{cm} \)

Step 4: Conclusion.
The height of the water level in the tank is 24 cm.

Final Answer:
The correct option is (C): 24 cm.