Grades 9-10 Video Solutions 2010-Levels 9&10 Video Solutions 2010 problem4

Video Transcription

Question number four. Four identical cubes form the rectangular solid shown in the picture to the right.  We have four cubes stacked in two on top of one another to form a rectangular prism. Now the surface area of each cube is equal to 24 centimeters squared.  The question is what is the surface area of the solid?  So we know that a cube is made up of six sides  and together that's 24 centimeters squared. So let's say that here is a side of one of these cubes, let's call it S,  and if we multiply 6S, the answer is 24 centimeters squared, the surface area of one of those sides. So the surface area of one of those sides is exactly 4 centimeters squared.  And now how many sides are visible? We have one, two, three, and four on the front face of the solid, four on the back face, so that's 8S for the front and back.  Then we have on the top and bottom here, one and two on the top and on the bottom, two more, so plus 4S for the top and bottom. Let me move that over a little bit.  So that's for the top and bottom. And finally for the sides here, we have one and two again, so plus 4S, and this is for the sides.  And so we obtain, when we add this, 16S, and S is four, so that's 16 times 4S,  times 4 centimeters squared, or that gives us 64 centimeters squared as the surface area for the solid.  Counting the exposed sides and multiplying that number by the surface area of each side we have computed before,  64 to be 4 centimeters squared, and that gives us our answer, which is here, B, 64 centimeters squared.

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