Answer:
V= 76 π cubic units
Step-by-step explanation:
y= [tex](x-3)^{2}[/tex] -----> [tex]x=\sqrt{y} +3[/tex]
Here we will apply the risk method.
Risk method: consider a strip of length x and width dy as
a) Radius= R(y) = x = [tex]\sqrt{y} + 3[/tex]
[We rotate this disc about y-axis to get a disk]
b) Cross-section area = A(y)= π [tex](radius)^{2}[/tex]
= A(y)= π (y+9+6 [tex]\sqrt{y}[/tex])
--------> Volume of the disc = A(y) x dy
c) Required volume= v = [tex]\int\limits^4_0[/tex] A(y) x d(y)
V= [tex]\int\limits^4_0[/tex] π (y + 9 + 6[tex]\sqrt{y}[/tex] ) dy
V= π [ [tex]{\frac{y^{2} }{2} + 9y + 4y^{\frac{3}{2} }[/tex][tex]]_{0} ^{4}[/tex]
V= 76 π cubic units.
