Question

Can someone help me solve this problem?

Answer 1

`A=pi(r^2-h^2)`

Explanation:

If we let `hatr` be the radius of the circular cross-section (as opposed to simple `r`, the radius of the sphere,
then by the Pythagorean Theorem
`color(white)("XXX")(hatr)^2=r^2-h^2`

The Area of the circular cross-section is given by the standard formula for the area of a circle:
`color(white)("XXX")A=pi * (hatr)^2`

`color(white)("XXX"A)=pi * (r^2-h^2)`