Question

Please I need this asap, my answer is wrong

Answer 1

Answer: $512\pi$

Step-by-step explanation:

Given

Equation of curve is $x=\sqrt{8+y}$

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

$\Rightarrow V=\int_{-8}^{24}\pi (8+y)dy\\\\\Rightarrow V=\pi\left ( 8y+\dfrac{y^2}{2}\right )_{-8}^{24}\\\\\Rightarrow V=\pi \left ( 8\times 32+\dfrac{24^2-8^2}{2}\right )\\\\\Rightarrow V=512\pi$