Question

The base of a certain solid is the region enclosed by the semicircle x^2+y^2=9 for x is less than or equal to 0 and greater than or equal to 3. Every cross section taken perpendicular to the x axis is a semicircle with its diameter across the base. Find the volume of the solid.

Answer 1

the section of the ball is a circle 

then the solid is the fourth part of the ball

x²+y²+z²=9 R=(9)^1/2=3

V=4/3$\pi$R³ /4 = $\pi$R³/3=$\pi$(3)³/3= 9$\pi$