Answer:
The Volume of the solid
V = π(1365.33) cubic units
Step-by-step explanation:
Step(I):-
Given curves are x²- y² = 64 , x=0 , y=-8 and y=8
The given function x = f(y)
x²- y² = 64
x² = y² +64
The Volume of the solid generating by revolving the region bounded by the graphs of the equations
[tex]V = \pi \int\limits^a_b {x^2} \, dx[/tex]
Step(ii):-
the limits are y = a = -8 and y = b=8
The Volume of the solid
[tex]V =\pi \int\limits^8_8 {(y^2+64)} \, dx[/tex]
[tex]V = \pi (\frac{y^{3} }{3} + 64 y )_{-8} ^{8}[/tex]
[tex]V = \pi (\frac{(8)^{3} }{3} + 64 (8) - (\frac{(-8)^{3} }{3} +64(-8) )[/tex]
[tex]V = \pi (\frac{(8)^{3} }{3} + 64 (8) - (\frac{(-8)^{3} }{3} +64(-8) ) = \pi (\frac{1024}{3} + 1024)[/tex]
V = π(1365.33) cubic units
