You place a steel ball with diameter 4cm in a water-filled cylinder that is 5cm in diameter and 10cm high. What volume of water will spill out of the cylinder?
I'm lost....
opps, I gave you the volume of the sphere, which is the amount of water that will be displaced by the sphere. If the cylinder was filled, and the sphere dropped in, then the volume of the sphere is the volume of the water which spills over.
Do you know the formulas for the volumes of cylinders and spheres?
The volume of the cylinder does not enter into the problem.
As Bob pointed out, the dropped sphere will simply displace its own volume, which is
(4/3)π(2^3) = 32π/3 cm^3
The sphere could have been dropped in any container, a fruit bowl, a coffee can, or whatever
as long as the container was filled to the top.
To find the volume of water that will spill out of the cylinder when you place the steel ball inside, we need to compare the volume of the steel ball with the volume of the cylinder.
First, let's find the volume of the steel ball. The formula for the volume of a sphere is V = (4/3) * π * r^3, where "r" is the radius of the sphere. Since the diameter of the steel ball is given as 4cm, the radius will be half that, which is 2cm.
Using the formula, the volume of the steel ball is:
V = (4/3) * π * (2cm)^3
V ≈ 33.51 cm^3
Next, we need to find the volume of the water-filled cylinder. The formula for the volume of a cylinder is V = π * r^2 * h, where "r" is the radius of the base and "h" is the height.
The given diameter of the cylinder is 5cm, so the radius is half that, which is 2.5cm. The height of the cylinder is given as 10cm.
Using the formula, the volume of the cylinder is:
V = π * (2.5cm)^2 * 10cm
V ≈ 196.35 cm^3
Now, since the volume of the steel ball is smaller than the volume of the cylinder, the steel ball will displace some of the water, causing it to spill out.
To find the volume of water that spills out, subtract the volume of the steel ball from the volume of the cylinder:
Volume of spilled water = Volume of cylinder - Volume of steel ball
Volume of spilled water ≈ 196.35 cm^3 - 33.51 cm^3
Volume of spilled water ≈ 162.84 cm^3
Therefore, approximately 162.84 cm^3 of water will spill out of the cylinder when the steel ball is placed inside.
what is the volume of the cylinder?
4/3 PI r^3