a cylinder of radius 14 cm contains water. a metal solid cone of base radius 7 cm and height 18 cm is submerged into water.find the change in height of the water level in cylinder.
volume of cone = (1/3)π(7^2)(18) = ...
change in volume of cylinder by the cone = π(14^2)(h)
set them equal and solve for h
To find the change in height of the water level in the cylinder, we need to calculate the volume of the cone and then determine how much water it displaces.
Step 1: Calculate the volume of the cone.
The volume of a cone can be calculated using the formula: V = (1/3) * π * r^2 * h
Given the base radius (r) of the cone is 7 cm and the height (h) is 18 cm, we can calculate the volume as follows:
V = (1/3) * π * 7^2 * 18
V ≈ 539.3 cm^3
Step 2: Determine the change in height of the water level.
The displaced water volume is equal to the volume of the submerged cone. The change in height can be found by dividing the displaced volume by the base area of the cylinder.
The base area of the cylinder can be calculated using the formula: A = π * r^2
Given that the radius (r) of the cylinder is 14 cm, we can calculate the base area as follows:
A = π * 14^2 ≈ 616 cm^2
Dividing the volume of the cone by the base area of the cylinder gives us the change in height:
Change in height = Volume / Base area = 539.3 / 616
Change in height ≈ 0.875 cm
Therefore, the change in height of the water level in the cylinder is approximately 0.875 cm.