Question

Consider a sphere of radius R and two parallel planes that are a distance d < 2R apart and such that both intersect the sphere. Determine the surface area of the sphere caught between the two planes.

Answer 1

Surface area of a sphere is \(2\pi R^2\)
Surface area of a cap of a sphere is \(2\pi Rh\) where h is the height of the cap. In this case, it is R-d/2
But you have 2 caps.
Hence the area of the region between them is \(2\pi R^2 -2*(2\pi (R-h))\)
Replace and calculate, you can get the answer.

Answer 2

@Loser66 surface area of a sphere is \(\color{red}4\pi R^2\)

Answer 3

Thanks for correcting me @SithsAndGiggles