Question

Problem 3a

Answer 1

Given information

Given:

A segment of height of a sphere of radius is

              

Step-by-step explanation

Step 1.

(A) First we consider a circle of radius whose center at the origin 

Since (radius of circle)

And (given)

Then    

Are and respectively

Since the equation of the circle is

Then    

 

If we rotate the shaded region about  axis then we get a cap of a sphere with a height .

The radius of a typical disk is

Then cross-sectional area of the typical disk is