Answer = 321.7
Explanation:
radius = y
height = [tex]4y^{2} - y^{3}[/tex]
area of cylinder = 2π*r*h
Integrate the area to calculate the volume:
[tex]= \int\limits^0_4 {2\pi(4y^{3} -y^{4}) } \, dy[/tex]
[tex]= 2\pi (\int\limits^0_4 {4y^{3}dy -\int\limits^0_4 y^{4} dy )} \,[/tex]
[tex]= 2\pi (256-\frac{1024}{5} )[/tex]
[tex]=\frac{512\pi }{5}[/tex]
[tex]= 321.7[/tex]
