Use the givens (only the fluid volume is required for the solution).
Follow instructions in step 5 on the graphing calculator.
This is no beast. Just a word problem, using a calculator to find a minimum solution. Do not get overwhelmed.
fluid volume: 44 cm^3
cylinder hight: 5.1 cm
cylinder diameter: 3.8 cm (radius = 1.9 cm)
Cap height: 4.1 cm
Cap diameter: 3.8 cm (radius = 1.9 cm)
Box: 13.3 cm x 7 cm x 4.1 cm
(1) circumference (function of r) ?=
(2) Area of cylinder side surface = curcumference x height, S_side(r,h) ?=
(3) End surface area = area of disk (function of r) S_disk(r) ?=
(4)Area of cylinder function of r and h = side surface area + (2 x end surface area), S_cyl(r,h) ?=
(5) Volume of cylinder function of r and h = area of disk x height, V(r,h) ?=
Height = fixed Volume / disk area
h as function of r, h = 44 cm^3 / disk area
(6) h =?
(7) Area = fixed volume / height, Area = 44 cm^3 / h
r as function of h,
(8) r ?=
Use equation (6) to replace h in (4)
(9) Area of cylinder as function of r, S_cyl(r) ?=
Use equation (8) to replace r in (4)
(10) Area of cylinder as function of h, S_cyl(h) ?=
Follow directions of step 5 with graphing calculator.