# Thread: Least Surface Area Problem

1. ## Least Surface Area Problem

2. Originally Posted by WartonMorton
I can't see any attachment

3. Originally Posted by earboth
I can't see any attachment
Sorry about that. I think I figured out how to attach it now.

4. Hi

Let R be the radius of the cylinder and L its length

The volume is $\displaystyle V_0 = \pi R^2L + \frac43 \pi R^3 = 13.4 cm^3$

From this expression you can find L as a function of R

The area is $\displaystyle A(R,L) = 2\pi RL + 4 \pi R^2$

Substitute L function of R to get A(R)

Calculate A'(R) to find the value of R which minimizes the area

5. Originally Posted by running-gag
Hi

Let R be the radius of the cylinder and L its length

The volume is $\displaystyle V_0 = \pi R^2L + \frac43 \pi R^3 = 13.4 cm^3$

From this expression you can find L as a function of R

The area is $\displaystyle A(R,L) = 2\pi RL + 4 \pi R^2$

Substitute L function of R to get A(R)

Calculate A'(R) to find the value of R which minimizes the area

I got 1.845, how does this match up to what you got?

6. I am getting 1.473 in

7. Originally Posted by running-gag
I am getting 1.473 in
Any body else got 1.845 or 1.473?

8. Originally Posted by WartonMorton
Any body else got 1.845 or 1.473?
The exact value of r is: $\displaystyle r = \frac{\sqrt[3]{10050}}{10 \cdot \sqrt[3]{\pi}} \approx 1.473461286$