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DaniilM [7]
3 years ago
12

Please I need this asap, my answer is wrong

Mathematics
1 answer:
zavuch27 [327]3 years ago
7 0

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

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