To find the change in height of the water level in the cylinder, we need to first calculate the volume of the solid hemisphere.
The volume of a solid hemisphere can be calculated using the formula:
V = (2/3)πr^3
Given that the radius of the solid hemisphere is 7 cm, we can substitute this value into the formula:
V = (2/3)π(7^3)
V = (2/3)π(343)
V = (2/3)(1078.47)
V ≈ 719.10 cm³
Since the solid hemisphere is submerged in the cylinder, the change in water level will be equal to the volume of the hemisphere.
Now, the volume of the cylinder can be calculated using the formula:
V = πr^2h
Given that the radius of the cylinder is 15 cm and the height is 24 cm, we can substitute these values into the formula:
V = π(15^2)(24)
V = π(225)(24)
V = π(5400)
V ≈ 16964.16 cm³
Therefore, the change in water level in the cylinder is approximately 719.10 cm³.
A cylinder of radius 15 cm and height 24 cm is filled with water. A solid hemisphere of radius
7cm is submerged into the cylinder and removed. Find the change in height of water level in
the cylinder. (4 marks)
1 answer