a cylinder of radius 14cm contains water. a metal solid cone of base radius 7cm an height 18cm is submerged into the water. find the change in height of the water level in cylinder.
3/2 or 1.5 cm
thank you but I kinda need the whole working. I got lost somewhere.
To find the change in height of the water level in the cylinder after the metal cone is submerged, we need to calculate the volume of the cone and compare it to the volume of water displaced by the cone.
Let's first calculate the volume of the cone:
Volume of cone = (1/3) * π * r^2 * h
where r is the base radius of the cone and h is the height of the cone.
Given values:
r = 7 cm
h = 18 cm
Volume of cone = (1/3) * π * (7^2) * 18
= (1/3) * 22/7 * 49 * 18
= 22 * 7 * 6
= 924 cm^3
Now, to find the change in height of the water level in the cylinder, we need to compare the volume of the cone (924 cm^3) with the volume of water displaced by the cone.
Since the volume of water displaced by the cone would be equal to the volume of the cone, the change in height of the water level would be the same as the height of the cone.
Therefore, the change in height of the water level in the cylinder is 18 cm.
To find the change in height of the water level in the cylinder, we need to calculate the volume of the cone and subtract it from the volume of the water initially in the cylinder.
1. Calculate the initial volume of water in the cylinder:
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
In this case, the radius of the cylinder is 14 cm. Since the cylinder is full of water, the height of the water is irrelevant.
Hence, the initial volume of water is V_initial = π * (14 cm)^2 * h_initial.
2. Calculate the volume of the cone:
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height.
In this case, the radius of the cone's base is 7 cm and the height is 18 cm.
So, the volume of the cone is V_cone = (1/3) * π * (7 cm)^2 * 18 cm.
3. Calculate the change in volume of water:
The change in volume of water in the cylinder can be found by subtracting the volume of the cone from the initial volume of water:
ΔV_water = V_initial - V_cone.
4. Calculate the change in height of the water level:
Since the initial volume of water is π * (14 cm)^2 * h_initial and the change in volume of water is ΔV_water, we can use the formula for the volume of a cylinder to find the change in height:
Δh = ΔV_water / (π * (14 cm)^2).
By following these steps and plugging in the given values, you can calculate the change in height of the water level in the cylinder.