Aug 23, 2022

# 11 Find Dimensions of Rectangular Prism Given Its Volume

Here's a very nice flexible question, you'll understand why I say this and here we're going to use a method we call back calculations and in this particular example we're going to examine the

of a

## rectangular

### prism

. Now back calculation is a great technique for solving Extremely Difficult Math Problem You realize it is a very effective technique. question before us. The

of a

## rectangular

### prism

is a 24 cm cube. determine the possible

of the

### prism

but we are supposed to

all possible

of a

## rectangular

### prism

#### dimensions

means length width and height ok let me make a

## rectangular

### prism

right so let's say they say this is our

## rectangular

### prism

and i prefer to draw like this so I always start from the top, the reason is very simple, you will understand right now that the side that we can't see should be correctly dotted, so if I start from the bottom it's very difficult, with a dotted line to begin, which is easy to connect the dots.
Do you see that it now looks more or less like a

## rectangular

### prism

? Let's say this is my length this is the width and this is the height of this rectangle

what is the

let's say

### volume

V is equal to length times width times height so you can put a dot in between that means that too Times, or you can put crosses, that's fine, but what we gave here is that the

### volume

is 24 centimeters cube, that's what we got, and you need to

### find

out what length, width and height that could be, that's very difficult.
One thing is very obvious is that the units are in centimeters so we can write well that's also in centimeters so we know that much at least I've seen sometimes we're missing that right now we need to look at what combination from length width and height could give us 24 when multiplied that's what the real question is so what I'll do for you I just make a little table so let me draw these lines here and then say well i need to multiply three numbers and i get 24 how do i get there so that becomes the real question so let's assume the length is 24 even if my length is 24 which 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 it This trick is awesome so let's try half of 24 for example let's say 2 12 and 12 times - let's give 2 for the width becomes 24 and keep one for the height, that's awesome , that's another condition how about 6 and this time 6 times 2 is 12 and let's do Hiders 2 which is also 24 you'll

### find

that we can go on for so long it's going to be a very long combination of numbers right , so add numbers like that and

### find

out how many combinations you can provide me with so I can have a

## rectangular

with a

### volume

of 24 cm cube you imagine yes I could have written here like 4 times 3 is 12 and 12 times 2 is 24 so I can get so many combinations right and so I can continue my list.
Wow I can end up with probably ten 20's I don't know how many maybe hundreds of solutions like this who knows there could be many solutions so work it out and let's see who has the max number of solutions for this problem gets so you realize that problems can have more than one solution right, it's entirely up to us how we see or solve them. I hope you enjoy this thank you and all
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