Answer:
[tex] V = 4[18 -(-18)]= 4*36 =144[/tex]
Step-by-step explanation:
the figure attached shows a square cross section with area [tex] r^2[/tex]
If we solve for y in terms of x from our equation we got:
[tex] y= \sqrt{9-x^2}[/tex]
We assume that the area for the square corss section is given by [tex] A = r^2[/tex]
And the total area for the cross section selected is:
[tex] r = 2\sqrt{9-x^2}[/tex]
So then we can express tha area on thse terms of x is given by:
[tex] A(X)= [2\sqrt{4-x^2}]^2 = 4 (9-x^2)[/tex]
And now we can find the volume using the followin integral:
[tex] V =\int_{-3}^3 4 (9-x^2) dx[/tex]
[tex] V= 4[9x - \frac{x^3}{3}] \Big|_{-3}^3 [/tex]
And evaluating using the fundamental theorem of calculus we got this:
[tex] V =4[27 -(-9)]= 4*36 =144[/tex]
