Find the volume of the solid whose base is the region bounded between the curve...?

Question

Find the volume of the solid whose base is the region bounded between the curve y = x^2 and x-axis from x=0 to x=3 and whose cross sections taken perpendicular to the x-axis are squares. (Do not round your answer.)

Thanks for the help! Always appreciated.

Answer 1

Every section of the solid will be a rectangular prism of length x, width x, and a height of the change in x. The x's of the length and width are determined by what x^2 equals at that point, so...

Upper limit 3, lower limit 0 for the integral (x^2)^2dx
Or just (x^4)
so the integral will be 1/5 (x^5) from 0 to 3
= 243/5

Answer 2

Are you revolving this area about an axis? Because if not that region seems more like an area.