Please explain better about creating volume. It takes less material to get say, a 1" cross section. A cylinder will touch at 4 points in a rectangular opening battery pack. A 1" square bottle or can holds more volume than a 1" dia. cylinder. 1 x 1 = 1 sq, inch pi r2 (0.05 x
0.05) = 0.785 sq. inch. A square battery could have more power packed in the space than a round (cylinder) shaped one.
First, when you are measuring the area of a cross-section, notice that you get inches^2, rather than inches. I use "in" below. If we have a string of length L forming a circle (of unknown radius r). Then L =
2*PI*r (circumference formula), so r = L/(2*PI), and consequently the area of the cross section is (from the area formula) A_1 = PI*r^2 = PI *(L/(2*PI))^2 = L^2/(4*PI) in^2.
The area of a rectangle having perimeter L is maximized when the rectangle is a square (that's a separate problem I won't go into now). However, in this case, where we have a square cross section, we we get side length s = L/4, so A_2 = (L/4)^2 = L^2/16 in^2.
We conclude that A_1/A_2 is about L^2/(4*PI) /(L^2/16)= 16/(4*PI) = 4/PI is about 1.27.
So A_1 is about 1.27 times the area of A_2.
Note that the result, does not depend on the value of L. Let me know if you have any questions or if you find an error (they happen!) : )
He's showing that you get maximum area with a given length bit of string if you arrange it in a circle rather than a square. This also means that if you battery is constant cross-section, as an AA is, the best shape for it to have to minimise the amount of case-material used to make it, is a cylinder.
From the point of view of minimizing the use of materials for an enclosure, the *sphere* does best. And, I can't think of any reason why this wouldn't be a great design (ha!) ; )
On Fri, 22 Sep 2017 20:22:18 +0100, Tekkie=AE wrote= :
re square in crosssection, they wouldn't roll off the desk.
At least I don't roll away. Place an AA on your desk, attempt to touch = the ends with a multimeter. Chase battery around the desk, pick it up o= ff the floor, then try again.
-- =
"Beam me aboard, Scotty!" [-] "Will a 2 X 4 do, Captain?"
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