Answer:
200π cubic units.
Step-by-step explanation:
Use the general method of integrating the area of the surface generated by an arbitrary cross section of the region taken parallel to the axis of revolution.
Here the axis x = 9 is parallel to the y-axis.
The height of one cylindrical shell = 8 - x^3.
The radius = 9 - x.
2
The volume generated = 2π∫ (8 - x^3) (9 - x) dx
0
= 2π ∫ ( 72 - 8x - 9x^3 + x^4) dx
2
= 2 π [ 72x - 4x^2 - 9x^4/4 + x^5 / 4 ]
0
= 2 π ( 144 - 16 - 144/4 + 32/4)
= 2 π * 100
= 200π.
