Answer to Question #291323 in Civil and Environmental Engineering for Heiya

Question

Find, approximately, the amount of metal in a closed tin can 3 inches in diameter and 5 inches

high, if the metal is 1/32 inches thick.

Answer 1

For this problem, we're going to create an open topped box, starting with a flat sheet off plate metal. Now, from this sheet metal, we're going to cut out a square from each corner. That is three inches on a side. Okay, now we're told a few things about this piece off this rectangular piece of sheet metal. First, we're told that the short side is X, and we know that the longer side is 2.5 times its width. So if the shorter side is X than the full longer side, before we cut out the squares is going to be 2.5 times X. It's 2.5 times as long as it is wide. Are there any restrictions on the size of this rectangular piece of metal? Well, we don't have an upper limit. We've even. This could be an enormous square for all we know, but we do have a lower limit, since I'm taking out three inches for each of these two squares in the corner, X has to be big enough to take out six inches, so X has to be greater than six inches. Like I said, there's no upper limit excessive have to be smaller than a certain amount, but it has to be at least a big as six inches. Okay, With that in mind, let's figure out what the volume of our resulting box will be. Well, I know that the base of the box and I'm gonna draw this in blue on my picture here. When I fold up the sides on those blue dotted lines, that's going to be the base of my box. So the short side is going to be X minus What I've removed from those corners X minus six. The long side is gonna be what I started with 2.5 and I'm going again. Subtract 63 for each of those squares in the corners. So I'm going to have 2.5 look. Sorry, not 2.52 point five X is what I started with 2.5 X minus six. And the height of my box will be three, cause that's what I'm cutting out. When I fold up those size, they're gonna be up three units from the base of my box. So let's multiply this out if I multiply those first two numbers all use foil to expand that out. I get 2.5 x squared, minus six x minus 15 X plus 36 and I'll be molting multiplying all of that by three. So that gives me off resulting volume equation of 7.5 x squared well, six x and 15 x is negative 21 x and then multiplying that by three. So naked is 63 x +108 This is my volume equation for this box. Therefore, the correct figure is 608 100 cubic inches.