QUICK QUESTION: Minimizing Restrictions

  • Thread starter Thread starter banfill_89
  • Start date Start date
banfill_89
Messages
47
Reaction score
0

Homework Statement



Question: a box with a square base and no top must have a volume of 10,000cm^3. if the smallest dimensions in any direction is 5cm, the determine the dimensions of the box that minimize the amount of material used.

Homework Equations



V=x^2&y
SA=x^2+4xy
(isolate for y using given volume in V equation to obtain y=10,000/x^2)

The Attempt at a Solution



SA=x^2+4x(10,000/x^2)

when solved...x=27.1
y= 13.6I have an answer on what the dimensions are, but what do i use as my limitations besides what my x values are. I know i have to use x>or=5...for some reason i can never figure these limitations/restrictions out...
 
Last edited:
Physics news on Phys.org
"must have a volume of 10,000cm^3" Sounds like a restriction to me.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Minimizing the surface area of an open box
Replies
11
Views
5K
Question re: Limits of Integration in Cylindrical Shell Equation
Replies
24
Views
3K
Rate at which a bucket gets filled
Replies
4
Views
2K
Restriction with Multiple Quantifiers
Replies
2
Views
2K
A few questions to make sure I understand Fourier series
Replies
3
Views
2K
Using differentials to estimate the maximum possible error
Replies
2
Views
2K
What Dimensions Minimize Material in a Paper Cup Designed for 8oz?
Replies
3
Views
1K
Volume of Revolution: Find V with Shell Method
Replies
13
Views
2K
Find the dimensions of the rectangle of greatest area
Replies
11
Views
8K
Maximizing Volume: Finding Optimal Dimensions for a Box with an Open Top
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top