Answer: [tex]512\pi[/tex]
Step-by-step explanation:
Given
Equation of curve is [tex]x=\sqrt{8+y}[/tex]
When this curve is rotated about the y-axis, then volume generated is given by
[tex]V=\int_{a}^{b}\pi x^2dy[/tex]
When [tex]x=0[/tex], [tex]y=-8[/tex]
Put the limits and solve the integral
[tex]\Rightarrow V=\int_{-8}^{24}\pi (8+y)dy\\\\\Rightarrow V=\pi\left ( 8y+\dfrac{y^2}{2}\right )_{-8}^{24}\\\\\Rightarrow V=\pi \left ( 8\times 32+\dfrac{24^2-8^2}{2}\right )\\\\\Rightarrow V=512\pi[/tex]
