The picture is he only information given to me. I found the Surface areas already, but the next question is to find the volumes of both the lines, reotated around both axis (so 4 questions).
I did Pappus Theorem for Line B around y axis, and got 72π. I'm however lost on the rest.
Line B rotated about the X axis just makes a washer. How am I to find a volume of something that has no thickness (doesn't travel about the x axis? Isn't it 2 dimensional?
And Line A confuses me completely. Using Pappus Theorem, I have to find the shape area that the lines make against each axis? (which seems to be a rhombus?), and then the centroid of that shape and the distance it travels to the axis? How do I even find that?
Partial answer (for the analytic part): Rotating a curve around the y-axis, you may compute the volume when the curve is given as $x=g(y)\geq 0$, $a\leq y\leq b \ $ by the formula $$\int_a^b \pi g(y)^2\; dy$$ A similar formula for a function $y=f(x)$. For curve $B$ indeed there is zero volume. For the last part I probably don't understand the questions...