 Let us look at how we can find out the volume of annular object and like a cylinder that you can see here and annular object is a hollow object but there is some thickness to it and what we are interested in finding out is this volume of the thick part and as you can see this is a cylindrical annular object with a blue border showing the outer layer and the yellow border showing the inner layer of this object. If we look at individually the blue object is also a cylinder and if we just look at individually the yellow object is also a cylinder just that this is a larger cylinder and the yellow one is a smaller cylinder. In order to get the volume of the annular object that we see here which is a cylinder a hollow cylinder rather we can do it by finding out the volume of larger cylinder minus the volume of smaller cylinder. Now let's just take an example by assigning radii to the larger cylinder and the smaller cylinder. Let's say that the radius of the larger cylinder is 12 centimeter and the radii of the smaller cylinder be 5 centimeter and let's say the length of the cylinder or rather when you keep it upright it will be called as a height and let's say this length or height of the cylinder is 30 centimeter. Now to get the volume of this annular cylinder we can put in the values as follows. So the volume of the larger cylinder will be pi times 12 square times the length of the cylinder L which is 30 minus pi times 5 square times 30. Now what is this pi times 12 square and pi times 5 square? This is basically pi r square which is the surface area of the circular base or circular region for the larger cylinder and and a smaller cylinder respectively. Since the radii are 12 and 5 we have pi times 12 square and pi times pi square. Now we can take pi and 30 out of the bracket by writing 30 pi and we can write 12 square minus 5 square. This will be equal to 30 pi times 144 minus 25 and that gives us 119 pi times 30 which is 3570 pi centimeter cube and this is how we can find the volume of the annular cylinder. Now what if we had an annular sphere with the outer sphere and an inner sphere given that the radius of the outer sphere is say 10 centimeter and radius of the inner sphere being 6 centimeter. How can we find the volume of annular sphere? Again we will look at the larger sphere and the smaller sphere and the volume of the annular sphere would be volume of larger sphere minus the volume of smaller sphere with the given values. We will apply the volume of the sphere formula for the larger sphere which is 4 by 3 pi times radius cube. The radius is 10 so we will write 10 cube minus we will write 4 by 3 times pi times the smaller radius cube and the smaller radius is 6. In order to solve this we can take out 4 by 3 pi common out of the brackets and just compute 10 cube minus 6 cube. This gives us 4 by 3 pi times the cube of 10 is 1000 and cube of 6 is 216 and this gives us 4 by 3 pi times 784 and this basically is equal to 3136 pi by 3 and the unit will be centimeter cube and this is how we can find the volume of the annular objects like sphere and cylinders.