We recognise that this is an ellipse. The question tells us to draw the first quadrant area only.

Ellipse to be rotated around axis

From the diagram, we can see that the limits of the bounded area are y = 0 and y = 1.

Hence the volume generated is:

`{: ("Vol",=pi int_c^d x^2 dy), (,=pi int_0^1 (4-4y^2) dy), (,=pi[4y-(4y^3)/(3)]_0^1), (,=pi[4-4/3] - pi[0]), (,=(8pi)/(3)\ text[units]^3), (,~~8.378\ text[units]^3) :}`