Volume of a Cylinder and Volume of a Right Circular Cone

Volume of a Cylinder Volume of a Right Circular Cone

Just as a cuboid is built up with rectangles of the same size, we have seen that a right circular cylinder can be built up using circles of the same size. So, using the same argument as for a cuboid, we can see that the volume of a cylinder can be obtained as:
base area × height  = area of circular base × height = πr²h

Where r is the base radius and h is the height of the cylinder.
In Fig, can you see that there is a right circular cylinder and a right circular cone of the same base radius and the same height?

Activity: Try to make a hollow cylinder and a hollow cone like this with the same base radius and the same height (see Fig). Then, we can try out an experiment that will help us, to see practically what the volume of a right circular cone would be!

So, let us start like this.
Fill the cone up to the brim with sand once, and empty it into the cylinder. We find that it fills up only a part of the cylinder [see Fig (a)].
When we fill up the cone again to the brim, and empty it into the cylinder, we see that the cylinder is still not full [see Fig (b)].
When the cone is filled up for the third time, and emptied into the cylinder, it can be seen that the cylinder is also full to the brim [see Fig (c)].
With this, we can safely come to the conclusion that three times the volume of a cone, makes up the volume of a cylinder, which has the same base radius and the same height as the cone, which means that the volume of the cone is one-third the volume of the cylinder.

Where r is the base radius and h is the height of the cone.