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What is the 49 times table?
1x49=49 2x49=98 3x49=147 4x49=196 5x49=245 6x49=294 7x49=343 8x49=392 9x49=441 10x49=490 11x49=539 12x49=588
If you have different shaped objects that weigh 1 kg would they have the same area?
Oh, No.The surface area of an object depends on its shape, not on its weight.Let me illustrate with one example:Let's say we have a regular cube made of aluminum. It weighs 1 Kilogram.It's size is 7 cm X 7 cm X 7cm (roughly 2.8 inches per side).Its volume would be 7x7x7 or, 73 = 343 cm3The surface area of that cube is the sum of the areas of its six sides:6 times (7 X 7) = 6X49= 294 cm2Now, if we took that cube of aluminum and forced it through a machine to change its shape, say two big heavy rollers, you could turn that cube into a long ribbon. (aluminum is a good example because you can easily do that with it).If we make sure no material is added or substracted, we would now have a long ribbon that would weigh exactly 1 Kg, and would look like a ruler.The important thing to know is that the volume of the aluminum has not changed, so, whatever the three sides of this ruler measure, the volume has not changed. It is still 343 cm3We stretched the aluminum so that now is a ribbon 76 cm long, 5 cm wide and 0.9 cm tall.This, in inches, is a ribbon roughly 30 inches long, 2 inches wide and less than a third of an inch thick, but guess what? it still weighs 1 Kilo.So, what would be the surface area of this ribbon? let's see:It is, again the sum if the areas of the six sides, but, since they are not the same, it gets a little tricky to run the numbers:2 sides are 76 X 5; which is 2 X 380 = 7602 sides are 76 x 0.9; which is 2 X 68.4 =136.8and2 sides are 5 X 0.9; which is 2 X 4.5 = 9The sum of all the areas is 760+136.8+9= 905.8!!So, just by changing the shape of a solid we changed the outside area from 294 cm2 to 905cm2;3 times larger area, same weight, same volume.
