Volume of a sphere

A hollow sphere and two cylinders whose base diameter and height are equal to the diameter of the sphere, sand.

- Fill the hollow sphere with sand once and empty it into one of the cylinders.
- Fill the hollow sphere a second time with sand and empty it into the second cylinder.
- Fill the hollow sphere a third time and empty it into the remaining spaces of the two cylinders.

**As performed in the simulator:**

- Generate a sphere of diameter 2r and two cylinders of height 2r each. Use checkboxes in the toolbox to generate a sphere and two cylinders.
- Click on "Next" to proceed. Use the sphere in the next step to fill both cylinders with sand.
- Now, click on the jug to fill the hollow sphere completely with the sand.
- The sphere is now completely filled with sand. Now, pour the sand from the sphere into the left cylinder. Place the sphere above left cylinder to pour the sand from the sphere into the cylinderClick again on the jug to fill the sphere with sand.
- Click on the jug again to fill the hollow sphere completely with the sand.
- The sphere is now completely filled with sand. Now, pour the sand from the sphere into the right cylinder. Place the sphere above right cylinder to pour the sand from the sphere into the cylinder
- Place the sphere above left cylinder followed by the right cylinder to fill them completely up to their brim.
- Follow the steps of derivation.

**Observations:**

- Students observe that the total sand emptied in three pourings fill both the cylinders completely.
- They, therefore, conclude that 3 times the volume of sphere = 2 times the volume of cylinder = 2 π r
^{2 }h = 4 π r^{3}( h = 2r)

Volume of sphere = 4\3 π r^{3}