That is true because you are still dividing x by three either way
The answer is 5× if is wrong sorry might help you
Since the formula for the base of the cylinder is

, multiplying that by 10 we get

. Hope this helps!
I've attached a plot of one such cross-section (orange) over the region in the x-y plane (blue), including the bounding curves (red). (I've set

for this example.)
The length of each cross section (the side lying in the base) has length determined by the horizontal distance

between the y-axis

and the curve

. In terms of

, this distance is

. The height of each cross section is twice the value of

, so the area of each rectangular cross section should be

.
This means the volume would be given by the integral