Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10

# Volume of a Right Circular Cone

## Notes

Activity : Try to make a hollow cylinder and a hollow cone like this with the same base radius and the same height  in following 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 above 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 above 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 above fig.(c)).
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.

So, Volume of a Cone = 1/3 πr^2h

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

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