I was wondering if I could elicit some help with this problem. I feel as if I understand it but cannot get the right answer.

It is number 21.

These are the steps I took:

- ΔF=(62.4ft/cm^3)(volume)
- =(62.4)(1/3 π r
^{2}h)- Since this is a cone, the radius isn't constant. I imagined that the come was made by revolving the integral x=2/3 y about the y axis, which then gives the r at any given height, Δy
- ΔF=62.4(1/3 π (2/3y)
^{2}Δy)- = 9.244π* y
^{2}Δy- Then
- ΔW=ΔF*d
- Let d= 6-y
- ΔW=(9.244π* y
^{2}Δy)(6-y)- W=9.244π*int [0, 6] 6y
^{2}-y^{3}- =9.244π(432-324)
- =998.352π

However the correct answer is 2995.2π...

Thank you in advance!

By the way I'm doing this on my phone so if the formatting is terrible, I'm sorry I'll try and revise it.