Question

Help please?!

Answer 1

Please see below.

Explanation:

(a) Let `r=` the radius of the water surface.

Extend the height of the water to the top of the hemisphere.
The length of the segment from the water surface to the top of the hemisphere is `10-h`

Draw a radius from the center of the top of the hemisphere to the point where the water surface touches the hemisphere. The radius is `10`.

You are now looking at a right triangle with legs `10-h` and `r` and with hypotenuse `10`.

So, `r^2 = 10^2-(h-10)^2 = 20h-h^2`

The surface are is `A = pi(20h-h^2)`

(b) Differentiate w.r.t `t`,

`(dA)/dt = pi(20-2h)(dh)/dt`

Substitute what you know and find `(dA)/dt`