Surface area of a sphere

Hollow sphere cut into two hemispheres, a cylinder with both base diameter and height equal to the diameter of the sphere

1. Take a roll of a jute thread and wind it closely on the surface of the hemisphere completely.

2. Take another roll of jute thread and wind it completely along the curved surface of the cylinder.

3. Compare the length of the two threads.

1.Check the two checkboxes in the toolbox to generate hemisphere and cylinder.

2.Now, click on "Next".

3.Drag these jute threads of length L over these figures to wind them completely.

4.Now, we will compare the length of two threads used to wind hemisphere and cylinder.

5.Proceed with the "Next" for derivation.

1. Students observe that the length of the thread used to cover the curved surface of the cylinder is twice the length needed to cover the hemisphere.

2. Since the thickness of the thread is uniform and the same for both the threads, surface areas are proportional to the lengths of the threads approximately.

3. Hence surface area of the hemisphere = half the surface area of the cylinder

=1/2 × 2 π r h

= π r h

= π r × 2 r ( h = 2r)

= 2 π r^{2}

Therefore, surface area of a sphere = 4 π r^{2}