What is the volume when you fold this into a box?

keep your decisions in mind i am a preshtalwalker the diagram illustrates a grid of an un

fold

ed rectangular box the diagram has dimensions of 13 10 and 34 as shown

what

is the

volume

of the rectangular box thanks to ketechie for suggesting

this

problem pause the video if you want me would like to try

this

problem and

when

you are ready, keep watching to learn how to solve

this

problem. So how can we solve

this

problem? We'll start by color coding the opposite faces of the rectangular box. We will then

fold

these faces together to create a rectangular box

this

three dimensional shape has a length equal to l a width equal to w and a height equal to h then we will un

fold

the faces to return to the grid we can then label the lengths on

this

diagram we will label some sides l other sides like h and

this

remaining side is w from here we have 34 equals 2l plus 2h then we have 13 equals w plus l and finally we have 10 equals w plus h we have a system of three equations for three variables let's start by dividing the first equation by two, then we'll subtract the third equation from the second equation and we'll get three equals l minus h we'll add these two resulting equations together and eliminate the variable h to get the 20 equals 2l

this

means l equals 10. we can substitute in the second equation to solve that w is equal to 3 then we can substitute in the third equation to solve that h is equal to 7. then po let's use these dimensions solve the

volume

of the rectangular box which is equal to l times w times h and that equals 210 it was quite a challenging problem but with a little bit of thinking in and out of the box we were able to solve it fairly routinely thanks for taking keep your decisions in mind one of the best youtube channels as always thanks for watching and thanks for your support