Question

why is the surface area of sphere is 4 times the area of circle​

Answer 1

Answer:

Step-by-step explanation:

If you think about the cylinder that just encloses the sphere, the area of the cylinder without the caps is just 4 \pi r^2, which is the same as the sphere. That is not a coincidence. If you consider a very thin horizontal slice of height h, the area of its intersection with the cylinder is 2 \pi r h. Now if a is the angle of the intersection of that slice with the sphere above (or below) the horizontal, we have height h / cos a and radius 2 \pi r cos a.

You will notice that the cosines cancel, so the area of the slice on the cylinder is the same as the area of the slice on the sphere.