Find the standard formulas for area of disks and cylinders and for volume of cylinders. You should already know these formulas or how to compute them from basic geometry.

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.

Givens:

fluid volume: 44 cm^3

fluid container:

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

Equations:

(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 =?

or

(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) ?=

or

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.

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