Question 796887: A monument consists of two cubical blocks, the smaller resting on the larger. The total height of the mmonument is 5 feet, and the area of the exposed surface is 61 square feet. Find the dimensions of the blocks.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Drawing a little picture, you can see that, on the bottom block, you can see 4 complete faces of the cube presuming you would actually be able to walk around it. If we let  represent the measure of the edge of the larger cube, then the surface area of each of the faces that can be seen in their entirety is  , so the total of those areas is  . The top block, which edge we will refer to as  , has the four sides and the top visible, so that part is represented by  . That leaves the partially exposed top face of the bottom block to account for. If the top cube wasn't there, the exposed area of the top face of the bottom block would be simply , but since it is partly covered by an area that amounts to  , the actual visible area is  . Putting the whole thing together:
\ +\ 4e_1^{\,2}\ +\ 5e_2^{\,2}\ =\ \ 61) .
Which is to say:
 .
Finally, since the total height of the stack is 5 feet:
Substituting:
^{\,2}\ =\ \ 61) .
The only thing left for you to do is to expand the binomial, collect like terms, put the quadratic in into standard form, and solve. Since represents the edge of the larger cube and the height is 5, the edge of the larger cube has to be larger than 2.5 feet. Hence, if you get a root that is smaller than 2.5 feet (and you will get one given correct arithmetic), discard it.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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