here is a very beautiful flexible question you will understand why i say that and here we are going to adopt a method that we call inverse calculus and in this particular example we are looking at the ### volume

of a ## rectangular

### prism

now inverse calculus is a great technique to solve extremely difficult mathematical problem . You realize that it is a very effective technique. The question before us is the ### volume

of the ## rectangular

### prism

. It is a cube of 24 centimeters. Determine the possible #### dimensions

of the ### prism

. Everything possible. That means you understand this kind of opening. but we are supposed to ### find

all possible #### dimensions

of a ## rectangular

### prism

#### dimensions

means length width and height ok let me make a ## rectangular

### prism

ok so lets say this is our ## rectangular

### prism

and i prefer to draw like this so i always start from the above the reason is very simple, now you will understand that the side that we cannot see must be dotted to the right, so if I start from the bottom and it is very difficult to start with a dotted line true that it is easy to connect the dots you see what more or less it looks like a ## rectangular

### prism

right now let's say this is my length this is width and that is the height of this ## rectangular

### prism

, so what is the ### volume

?

Say the ### volume

V is equal to length times width times height so you can put a dot in the middle which also means times or you can put crosses ok but what we are #### given

here is that the ### volume

is 24 centimeters. cube that's what they give us and you need to ### find

what length, width and height they could be that's very complicated one thing is very obvious the units are in centimeters so we can write it right all these are in so we can write this in centimeters and this is also in centimeters so we know at least sometimes I've seen us miss that right now we have to see what combination of length width height could give us 24 when multiplied that's the real question is then what am I to do? what i do is make a little table so let me draw these lines here and then i say ok i need to multiply three numbers and get 24 how can i get there so it becomes the real question so let's assume the length is 24 if my length is 24 what could be width and height well 24 times 1 is 24 so let's put one for each if you multiply these three you get 24 and all these units are in centimeters so it becomes a 24 centimeter cube hope you like that trick it's cool so let's try half of 24 for example we say 2 12 and 12 times - give 2 to width becomes 24 and keep one for height that's cool that's another condition how about 6 and this time 6 times 2 is 12 and let's hiders 2 which is also 24 you'll realize that we can go on like this for so long it's going to be a very long number combination so keep adding numbers like that and see how many combinations you can provide.

I with so I can have a ## rectangular

### prism

with a ### volume

of 24 cubic centimeters can you imagine yes I could have written here like 4 times 3 is 12 and 12 times 2 is 24 so I can give as many correct combinations and so I can continue my list Wow I may land with probably tens of 20 I don't know how many maybe hundreds of solutions like this who knows there could be many solutions so figure it out and let's see who gets the maximum number of solutions for this problem so they Please realize that problems can have more than one solution, it all depends on us, how we see or solve it, I hope you enjoy it, thanks and all.

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