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I have already calculated the volume (I hope my answer is right). However, I'm having a little trouble deciding which one of the "Sketching the solid, and a typical disk or washer." is correct? Can some one help me?

Please view attached pictures (Zoom to Enlarge):

enter image description here

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  • $\begingroup$ The cone is your best bet. $\endgroup$ – BenCarson2016 Nov 1 '15 at 22:36
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The top left figure on sketch the region corresponds to the bottom right figure on sketch the solid. The top right figure corresponds to the top left figure. The bottom right figure corresponds to the top right. The bottom right figure corresponds to the bottom left figure. So the top right figure in sketch the region should be the top left of sketch the solid. It can be checked be looking on the x and y coordinates such as if the shaded region only reaches x=8 then the solid figure can only reach x=-8,8.

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These two together are correct:

enter image description here

At lest these two belong to the given volume: $\frac{512\pi}{15}.$ These two belong to the equations given: $y^2=2x$,$x=2y$.

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