I need to find out the answer for the below math question.

Find the exact volume in cubic units generated by rotating a region, R, around the
y-axis, given that R is the region bounded by the curve y = x³ and the lines x = 1 and
y = 8.

Your help would be appreciated.
Thank you.
Colleen
for secondary school
parent of student

Hi Colleen,

I plotted a sketch of y = x³, y = 8 and x = 1 and shaded the region R.

The region shaded orange is the region you need to revolve around the y-axis. Either the disk or shell method will work but I think in this situation the cylindrical shell method results in an easier integral.

To use the cylindrical shell method take a vertical slice through the region R of thickness x and revolve this slice around the y-axis.

Is this enough help? Let us know.
Penny