working out area, bad at maths please help!?

Question

I'm trying to work out how many sheets of stainless steel i need, i am building an electrolysis cell (to turn water into hydrogen) anyway my maths is really bad, there are 72 plates needed (36 anodes and 36 cathodes (+/-)) each plate is the same and measures 12cm by 15cm. the sheets of stainless steel come in the following sizes; 2mx1m or 2.5mx1.25m or 3mx1.5m so how many sheets do i need and of which size (ie the one that has the least wastage).
I think i need 5 sheets of 2m*1m but im not sure im confused because the area of each plate (12*15 = 180cm2) but when i try and work out from 180cm2 i get big numbers and get confused! please help!

Answer 1

Answer: 1 sheet of the smallest size (2m x 1m) yields 104 plates if cut along the proper direction. (96 plates if you cut from the wrong direction)

Ok.... let's break this problem down...

You need 72 steel plates of size 15cm x 12cm

You choice of steel sheets come in three varieties:
a) 2m x 1m (200cm x 100cm)
b) 2.5m x 1.25m (250cm x 125cm)
c) 3m x 1.5m (300cm x 150cm)

Let's examine each size sheet and see how many of your plates can be made from each:
a) 2m x 1m:
Long side: 200cm /15cm = 13.333 rows of plates
Short side: 100cm /12cm = 8.333 plates per row

Obviously you can't have partial rows or pieces so you need to leave off any remainder
That leaves 13 rows of 8 plates. That's 104 plates!!!

We don't need to examine any of the larger sizes because 1 sheet of the smallest size is big enuogh for you with plenty to spare!

However for producing larger numbrs you may want to compare all the sizes:
a) 2m x 1m: 104 plates (5 inches to spare on the long side, and 4 inches to spare on the short side)

b) 2.5m x 1.25m: 160 plates (10 inches to spare on the long side and 5 inches to spare on the short side)
c) 3.0m x 1.5m: 250 plates (0 inches to spare on either side)(250 divides too perfectly you will only get 228 if you account for the extra you take off while cutting)**

**Please note that the this figure doesn't account for any width being cut off with each cut because it divides perfectly evenly. You may wind up with less than 250 because you'll lose some width with each cut. That would put your plate numbers down to 228 for the largest sheet of steel because you'd have to leave room to lose a little width on each cut. All the other measurements leave at least a spare 4 inches to attain the maximum, but this one divided perfect on both side.

Also note that to acheieve the maximum number of plates stated you have to make sure you're cutting from the correct side. You want to make sure your 15cm side is coming out of the largest side for all scenarios except for the largest sheet (3m x 1.5m). In that case you could theoretically get 250 sheets when taking the 12cm out of the largest side and the 15cm out of the smaller side but as explained above you'd have no spare room to account for the width you cut out.
Since you have to account for the bit you're going to shave off it would be better to cut the 15cm out of the long side and the 12cm out of the smaller side, you will get 228 sheets instead of 216. If you cut from the wrong side you'll get less plates.

Answer 2

100 cm = 1 meter
10,000 cm^2 = 1 m^2
You need 12*15*72 cm^2 + Waste
or 12,960 cm^2 + Waste
or 1.296 m^2 + Waste
1m x 2m = 2 m^2 and should be sufficient.

Let's check. Let's cut the 1m x 2m piece into strips 15 cm high and 2 m long. That means we get 1*100/15 = 6 strips.
Now cut each 2 m strip into 15 cm pieces and get
200/15 = 13 pieces.

6 strips * 13 pieces / strip = 78 pieces. Since you only need 72, the 2m x 1m piece of stainless is big enough by itself
(assuming you can cut it accurately).

Answer 3

You should be able to use the 2m x 1m sheet. Since you were getting confused converting cm^2 to m^2 convert 12cm to .12m and 15cm to .15m. The area of each plate would then be .018m^2. You would be able to get 13 strips 15cm wide if you cut them along the 2m edge of the sheet. And you would be able to get eight 12cm lengths out of each of this strips. 13 * 8 = 104 which is way more that your required 72.

Good Luck

Answer 4

use 1 sheet of the 2m x 1m it will give you 96 plates. stop trying to figure out the area. you just need to look at it like a checker board. you can get 6.6 columns of 15 cm across the 1m side and you can get 16.6 rows of 12 cm down the 2m side which gives you a total of 96 plates as the .6 on both sides would be scrap.

Answer 5

You should be able to get them all onto just one sheet of the 1m x 2m. keep in mind that 1m = 100cm, so thats 100cm x 200cm (or 20,000 sq cm that you'll have to work with) if you orient the plates tall-wise with the sheet also tall wise, you should be able to get 8 across and have enough sheet to make 13 rows... 104 plates, with a little room for goofing up.

Answer 6

With the 3m X 1.5 m sheet you could make 250 Plates.That means you would use onl 28.8 % of5 the sheet.

With the 2.5m X 1.25m sheet , you could make 152 plates. this means you would use only 47% of one sheet.

With the 2m X 1m sheet, you could make 96 platelets. This would mean that you are using 75% of one sheet. This is clearly the best way to go.

Answer 7

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Answer 8

I thought you kids were wisses with a calculater use a few gray sells and work it out you have enough aids

Answer 9

use 1 big sheet to cover the hole area
then you will not burn out your brain trying to work it out