Difference between revisions of "2013 AMC 10A Problems/Problem 14"
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<math> \textbf{(A) }36\qquad\textbf{(B) }60\qquad\textbf{(C) }72\qquad\textbf{(D) }84\qquad\textbf{(E) }108\qquad </math> | <math> \textbf{(A) }36\qquad\textbf{(B) }60\qquad\textbf{(C) }72\qquad\textbf{(D) }84\qquad\textbf{(E) }108\qquad </math> | ||
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| + | We can use Euler's polyhedron formula that says that <math>F+V=E+2</math>. We know that there are originally <math>6</math> faces on the cube, and each corner cube creates <math>3</math> more. <math>6+8(3) = 30</math>. In addition, each cube creates <math>7</math> new vertices while taking away the original <math>8</math>, yielding <math>8(7) = 56</math> vertices. Thus <math>E+2=56+30</math>, so <math>E=84</math>, <math>\textbf{(D)}</math> | ||
Revision as of 15:55, 7 February 2013
A solid cube of side length 
is removed from each corner of a solid cube of side length 
. How many edges does the remaining solid have?
We can use Euler's polyhedron formula that says that 
. We know that there are originally 
faces on the cube, and each corner cube creates more. 
. In addition, each cube creates 
new vertices while taking away the original 
, yielding 
vertices. Thus 
, so 
, 
