Question

Please I need this asap, my answer is wrong

Answer 1

Answer:
`512\pi`

Explanation:

Given

Equation of curve is
`x=√(8+y)`

When this curve is rotated about the y-axis, then volume generated is given by

`V=\int_(a)^(b)\pi x^2dy`

When
`x=0`,
`y=-8`

Put the limits and solve the integral

`\Rightarrow V=\int_(-8)^(24)\pi (8+y)dy\\\\\Rightarrow V=\pi\left ( 8y+(y^2)/(2)\right )_(-8)^(24)\\\\\Rightarrow V=\pi \left ( 8* 32+(24^2-8^2)/(2)\right )\\\\\Rightarrow V=512\pi`