All right let’s look at volume of spheres. So in the problem, it states, a spherical ball is shipped in a cylindrical container which it just fits. Okay so here is our spherical ball in the cylindrical container. So we have two questions to answer, first what is the volume of the sphere in terms of π and then the second one, what fraction of the cylinder is occupied by the volume of the sphere.

All right, so let’s take a look at our first problem. All right here we need to find what is the volume of the sphere in terms of π. So when you’re looking for the volume of a sphere, the volume of the sphere is 4/3 x π x r³. So the volume of the sphere is 4/3 x π x r³. So from the sphere we know that the diameter of the sphere is 60 millimeters, so we know that the diameter is 60 millimeters and we also know that when you’re finding the radius which we need to know for our formula, the radius is half of the diameters. So 60/2 which would be 30 millimeters.

So now we have our radius we can go ahead and calculate the volume of the sphere. So the volume of the sphere is 4/3 x π x r³, so we have 4/3 x π which is 3.14, but actually we’re looking it in terms of pie so we’re going keep it x π x r which is 30³. And then if I calculate this, I get 36,000πmm³. So the volume of the sphere in terms of π is 36,000πmm³.

All right let's look at our second problem. All right so here what fraction of the volume of the cylinder is occupied by the volume of the sphere? So to find the fraction we first need to calculate the volume of the cylinder. So the volume of the cylinder can be calculated as such π x r² x h.

So for the cylinder, we already know what the radius is because we figured it out in our first problem. So we know that the radius is 30 millimeters and we know the height is 60 millimeters. So now we can calculate the volume of our cylinder. So the volume of our cylinder is then going to be π x r which is 30² x our height which is 60 and then we go ahead and calculate and we get 54,000πmm³.

All right, so now we have the volume of our cylinder. So now the fraction of the volume of the cylinder occupied by they sphere, so we’re looking for the fraction of the volume of the cylinder occupied by the volume of the sphere, we can figure that one out by taking the volume of the sphere and divided it by the volume of the cylinder.

So we know that the volume of the sphere that we got from the first problem is 36,000π, so we know that our volume of the sphere is 36,000π and then we know that the volume of our cylinder we just find out was 54,000π, so that means our fraction would be 2/3. So the sphere occupies 2/3 the volume of the sphere.

So something to keep in mind, from the above problem we can conclude that the volume of the sphere is 2/3 the volume of the cylinder or the same base radius and height. So from this we know that the volume of the sphere is 2/3 the volume of the cylinder of the same base radius and height.

All right so some things to keep in mind, some tips is remember that the volume of the sphere is 4/3 x π x r³. So the formula again is 4/3 x π x r³ and the volume of the sphere is 2/3 the volume of the cylinder of the same base radius and height. So remember when you have the same base radius and height the volume of the sphere is 2/3 the volume of the cylinder.