Who can solve this assessment question ?

[disdat111]

I have no idea how to work this question out:

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 ? (Hint: think of required surface area as a segment of a circle rotated about the x-axis).

Do you notice anything surprising about the answer? Whether you do or not, also determine the surface area of part of a cylinder of radius R between two planes that are distance d apart that are also parallel the base of the cylinder.
Do you notice something else that is surprising?


thanks alot sorry if in wrong section

 

[Deleted member 4993]

I have no idea how to work this question out:

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 ? (Hint: think of required surface area as a segment of a circle rotated about the x-axis).

Do you notice anything surprising about the answer? Whether you do or not, also determine the surface area of part of a cylinder of radius R between two planes that are distance d apart that are also parallel the base of the cylinder.
Do you notice something else that is surprising?


thanks a lot sorry if in wrong section

Since this is an assessment question - you should figure this out. A hint is given - where did you go with that hint.

Do you remember how to calculate surface area of revolution by integration? What will be the limits of such "definite integral" for your given problem?