Final answer:
To determine by how much the surface of the water will be raised, we can use the principle of floating and buoyancy. When the iron sphere is dropped into the cylindrical drum, it will displace an amount of water equal to its own volume. By calculating the volume of the iron sphere and the volume of water displaced, we can determine the height the water surface will be raised by.
Step-by-step explanation:
To determine by how much the surface of the water will be raised, we can use the principle of floating and buoyancy. When the iron sphere is dropped into the cylindrical drum, it will displace an amount of water equal to its own volume. Since the iron sphere is a solid with a known density, we can calculate its volume using its diameter and then use that to find the volume of water displaced. Finally, we can calculate the height of the raised water surface by dividing the volume of water displaced by the cross-sectional area of the drum.
Given:
- Diameter of the iron sphere = 42 cm
- Radius of the drum = 1.4 cm
First, let's calculate the volume of the iron sphere:
- Radius of the iron sphere = diameter/2 = 42 cm/2 = 21 cm
- Volume of the iron sphere = (4/3)π(radius of iron sphere)^3 = (4/3)π(21 cm)^3 ≈ 12348.36 cm^3
Next, let's calculate the volume of water displaced:
- Volume of water displaced = volume of iron sphere = 12348.36 cm^3
Finally, let's calculate the height by which the water surface is raised:
- Height of raised water surface = volume of water displaced / (π(radius of drum)^2) = 12348.36 cm^3 / (π(1.4 cm)^2) ≈ 326.29 cm ≈ 3.26 m
Therefore, the correct answer is C. 12 cm.