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Solution: How many 1 -cm squares would it take to construct a square t...

Question

How many 1 -cm squares would it take to construct a square that is 1 m on each side?

Video Transcript

Hey guys, in this question they're asking us how many 1-centimeter squares would it take to compile together to make a larger square that is 1 meter on each side? So, remember if we're talking about a square remember a square is the same length on all sides we'll each side is A so remember the area of a square equals A squared so here we want to construct a square that's 1 meter on each side so what would the volume of the square be? So if each side is 1 meter, 1 meter squared which is 1 meter that's squared would just be 1 meter squared but here we want to convert them all into centimeters because we're talking about centimeter squares that we're trying to make from this or make into this larger square so we're going to convert this 1 meter squared into centimeter squared so here we're going to put meters on the bottom centimeters on the top, remember that 1 is associated with the metric prefix so 1 centi is 10^-2 but remember, meters squared can't cancel out with meters like the way we want so we're going to square this entire thing, now what effect does that have? Squaring a power just means you're multiplying it so it's really -2*2 so this is really 1 meter squared times 1 centimeters square over 10x-4 meters squared, meters squared cancel out so we have 1.0x10^4 centimeters squared so that would be the area of the larger square that's 1 meter on each side now what we're going to have to do is figure out the area of a 1 centimeter square so it's the same exact process the area of this smaller square also equals A square so it would be 1 centimeter let's go on to B square so that's all we have there and then now what we're going to say here number of squares is we're going to say we're going to say we have a total of 1.0x10^4 centimeters squared for the larger square and then we're going to say that 1 centimeter square has an area of 1 centimeter squared, centimeter squares cancel out and we'll have how many squares is going to take, it will take 1.0x10^4 squares of these small squares stacked together to make the larger square, OK? So that would be the answer for this question very weird but this is the way you have to approach it, figure out the area of the larger square figure out the area of 1 individual small square and from there we can figure out how many do we need.