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.
Shaalaa.com | Volume of a Right Circular Cone
A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.
If the triangle ABC in the above Question is revolved about the side 5 cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained.
A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.
Find the capacity in litres of a conical vessel with height 12 cm, slant height 13 cm
The volume of a right circular cone is 9856 cm3. If the diameter of the base is 28 cm, find
(i) height of the cone
(ii) slant height of the cone
(iii) curved surface area of the cone
A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?