Question 787700
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?
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Volume of cylinder with diameter of base = d cm
V = (pi)*(d/2)^2 * h
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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
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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
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So the square-based prism has the smaller volume.
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Cheers,
Stan H.
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