1) The volume of the solid that results when the shaded region is rotated about the y-axis is ... a) $\frac{15}{2}\pi$ c) $2\pi$ b) $\frac{128}{5}\pi$ d) $30\pi$ Use the formula $V = \pi \int_a^b [W(y)]^2 - [V(y)]^2 dy$
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When rotated about the y-axis, the outer radius is $W(y) = 4$ and the inner radius is $V(y) = y^2$. The limits of integration are from $y = 0$ to $y = 2$. Show more…
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