Volume of a solid found by rotating the region around the y-axis

Question

Let R be the region in the first quadrant enclosed by the graphs of y=4x^2, x=1 and y=0. FInd the volume of the solid obtained by rotating the region R about the y-axis. Please express your final answer as a single number (not a sum or difference of numbers)

how do I solve this?

Answer 1

Answer 2

The volume of the cylinder is 4π

The volume of the paraboloid is the integral from 0 to 4 of (1/4)πy dy.

The volume required is the difference between these 2 volumes,