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

watch your decisions i am preshtalwalker the diagram shows a mesh of an un

fold

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

what

is the

volume

of the rectangular box thanks ketechie for pointing out

this

issue pause the video if you like Feel free to try

this

problem and

when

you are ready, keep reading to learn how to solve

this

problem. How can we solve

this

problem? We'll start by color-coding the opposite sides of the rectangular box, which we'll then

fold

those sides together to create a rectangular box.

This

three-dimensional shape has length l, width w, and height h.

We will then un

fold

the faces to return to the mesh. We can then label the lengths on

this

chart. We're going to label some sides like l other sides like h and that remaining side is w from here we have 34 equals 2l plus 2h we then 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, we will start by dividing the first equation by two. Then we subtract the third equation from the second equation and get three equals l minus h. We add these two resulting equations and eliminate the h variable, so we get that 20 equals 2l,

this

means l equals 10.

We can substitute into the second equation to solve that w equals 3. We can then plug in the third equation to solve that h equals 7. We can then use these dimensions. Solving the

volume

of the rectangular box, which is equal to l times w times h, which equals 210, was quite a challenging problem, but with a little thought inside and outside the box we were able to solve it quite routinely, thanks for making your choices as always one of the best channels on youtube. Thanks for watching and thanks for your support