Ahemispherical bowl of radius 12 inches is filled to a depth of h inches, where 0less than or equalshless than or equals12. find the volume of water in the bowl as a function of h. (check the special cases hequals0 and hequals12.)

Suppose the bowl is situated such that the rim of the bowl touches the x axis, and the semicircular cross section of the bowl lies below the x-axis (in (iii) and (iv) quadrant ). Then the equation of the cross section of the bowl would be , where y≤ 0,

⇒

Here, h represents the depth of water,

Thus, by using shell method,

The volume of the disk would be,

Special cases :

If h = 0,

If h = 12,

step-by-step explanation: