A large industrial type, cylindrical shaped vat measures 12 feet in diameter and that is 4 feet deep is capapable of containing a total capacity of 70% liquid. The chemical that fills the vat costs twenty-five cents per cubic inch retail. What is the wholesale cost of the chemical if the chemical has been marked up 20% and how much profit does the vendor make from selling the chemical at retail?

Wholesale Cost $____________ and Vendor Profit $______________


Thanks to all that find this fun and for your help in working it through.


ok to show im not here just to get answers. heres what i got so far

change my knowns to all same unit.
12ft = 144in
dia=144in rad=72in
4ft=48in

V=pi r^2 h
V=pi (72in)^2 (48in)
V=(5184in^2)(48in)(pi)
V entire capacity= (pi) x 248832 in^3
V 70% capacity=(pi) x 248832in^3 x (.70) = 174182.4(pi)
V=547210.148225in^3
Now to the hang up: I guess set this up as ratio? if you look back at my only other posted thread you will see why I am again stumped or at least need some pats on the back if im in the right direction. Not sure if im to use the ratio setup because of the whole profit and percentages I havent got hold of yet. Or is this just the price you paid; what is 20% of that subrtact the difference and that is the wholesale cost and you pay 20% more than that wholesale cost?

100/120 = x/ .25in^3; solve for x?
x=$.2083333333=amount per in^3 at wholesale cost? SO 21 cents? is my answer for wholesale cost per in^3.

547210.148225in^3 x ($.20833333333= wholesale cost of vat at its capacity, (which is only 70% of vat volume)
=$114,002.11 per vat?????? AND

Vendor Profit = $22,800.42 per vat??????