Question 787700: Hi,
I am having some trouble with a Geometry question for an investigation, which states:
What is the “best” container for mass production between a cylinder can and a square based prism with the same volume of 1000cm^3 ? and why?
I think it is the cylinder but i am not sure.
Thanks so MUCH!!!!!
Gabrielle
Found 2 solutions by stanbon, xinxin:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! What is the “best” container for mass production between a cylinder can and a square based prism with the same volume of 1000cm^3 ? and why?
--------
Volume of cylinder with diameter of base = d cm
V = (pi)*(d/2)^2 * h
--------
Volume of prism with diagonal of square base = d cm
If the edge is "x", x^2 + x^2 = d^2
2x^2 = d^2
x = sqrt(d^2/2) = d/sqrt(2) is the edge.
Then area of base = d^2/2
And Volume = [d^2/2]*h
-------
So volume depends on area of base, if height is the same for both.
Comparing [d^2/2] and (pi)[d/2]^2:::
d^2/2 "R" pi(d/2)^2
1/2 "R" pi/4
0.5 < 0.7854
---
So the square-based prism has the smaller volume.
=========
Cheers,
Stan H.
=========
Answer by xinxin(76) (Show Source):
You can put this solution on YOUR website! The statement is ambiguous...To me it seems like a business problem that you have to choose a container, which contains the least amount of mass, in order to have less expense. However, it doesn't say what kind of product is going to be produced.
If my inference was correct, then you would need the formula D = M/V (D: density of the material/product; M: mass; V:volume) to determine which container is the best.
|
|
|
