Rectangular Prism Surface Area

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ganjum2671

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A rectangular prism that is 13 inches in depth, 17 inches in width and 15 inches in height has two cutouts in it that are made with a square shape of side 3.8 inches. These cutouts go all the way through the block. What is the surface area of this shape?

SA2.JPG
 
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What is the surface area of a generic rectangular prism, in terms of its length (L), its width (W), and its height/depth (H)? (Refresher here if needed) Now pretend for a moment the prism didn't have anything cut out of it. What, then, is the surface area of this specific rectangular prism? It should be obvious that the surface area of the prism with the cutouts is going to be less than this value... but how much less, and why?

Can you see that the fact that the cutouts go all the way through the prism doesn't actually matter? And why the only parts of the cutout that reduce the surface area are the squares on the top surface and the bottom surface? How much area do these four squares have, in total? And what does that make the final answer for the surface area of the prism as a whole?
 
SA=2(wl+hl+hw) is the formula. Without the cuts the surface area is 1342. And with just the top and bottom portions of the square only the total would be 57.76? (Area is length*width so one square would be 3.8*3.8 or 14.44 which you would multiply by 4 to get the 2 on the top and 2 on the bottom.) And then you would subtract it from 1342, leaving you with 1284.24? but whenever I submit it, it says the answer is wrong.
 
The cutouts will remove surface area, but will also add surface area as well. What's not clear to me is along which dimension of the block the cutouts are parallel.
 
It looks like you missed the vertical sides of the holes. There are 8 rectangles there, each 3.8 by 15 (assuming the height is C).
 
If we follow the diagram, I suppose they are parallel to the height, and so while you need to subtract 4 squares 3.8 inches on a side, you also need to add 8 rectangle that are 3.8 X 15...
 
MarkFL said:
The cutouts will remove surface area, but will also add surface area as well. What's not clear to me is along which dimension of the block the cutouts are parallel.
Click to expand...
MarkFL said:
If we follow the diagram, I suppose they are parallel to the height, and so while you need to subtract 4 squares 3.8 inches on a side, you also need to add 8 rectangle that are 3.8 X 15...
Click to expand...
OH MY GOSH YOU'RE RIGHT!!! THANK YOU SO MUCH!! I GOT THE QUESTION RIGHT FINALLY!! I appreciate your help so much!!
 
MarkFL said:
If we follow the diagram, I suppose they are parallel to the height, and so while you need to subtract 4 squares 3.8 inches on a side, you also need to add 8 rectangle that are 3.8 X 15...
Click to expand...

Okay, I'm almost certainly having a brain fart or not seeing something here. How can a rectangular prism with some bits cut out have more surface area than the prism without the bits cut out?
 
Dr.Peterson said:
Because cutting down into the object exposes more surface to the air.
Click to expand...

D'oh! Right, right, how foolish of me to not see this before. Guess it just goes to show that even the "experts" are fallible too, and sometimes we don't know what the heck we're talking about.
 
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