# Thread: Crazy problem

1. ## Crazy problem

Greetings everyone,

my calc teacher thought it would be funny to assign an extremely hard problem for us to do because he was mad that the majority of the class failed an exam. So as punishment he wants us to figure out how to solve this problem which I don't really know why he would want us to do so considering he doesn't teach us anything! I'm currently reading over a few chapters, but I can't see to find any problem similar to the one he assigned. Anyway if anyone could possibly point me in the right direction and possibly help me with this insane problem I would greatly appreciate it.

Here is the beastly problem.

[img=http://img197.imageshack.us/img197/6732/krazyprobleml.th.png]
Thank you all for you time.

2. ## Find cylinder area as function of h and r

Originally Posted by Rainy2Day
Greetings everyone,

Anyway if anyone could possibly point me in the right direction and possibly help me with this insane problem I would greatly appreciate it.

Here is the beastly problem.

[img=http://img197.imageshack.us/img197/6732/krazyprobleml.th.png]
Thank you all for you time.
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.
...

3. thanks i'll try doing what you said.

4. For # 1. Surface Area = 2((π)(1.9cm)2)+(2π(1.9cm)) * (9.2cm) =132.51 cm^2

and for # 2. A= 2πr 2+2v/r

I'm not sure if I did number two right. If possible could anyone verify?