Difference between revisions of "2002 AMC 8 Problems/Problem 22"
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| − | Six cubes, each an inch on an edge, are fastened together, as shown. Find the total surface area in square inches. Include the top, bottom and sides. | + | ==Problem== |
| + | |||
| + | Six cubes, each an inch on an edge, are fastened together, as shown. Find the total surface area in square inches. Include the top, bottom, and sides. | ||
<asy> | <asy> | ||
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<math> \textbf{(A)}\ 18\qquad\textbf{(B)}\ 24\qquad\textbf{(C)}\ 26\qquad\textbf{(D)}\ 30\qquad\textbf{(E)}\ 36 </math> | <math> \textbf{(A)}\ 18\qquad\textbf{(B)}\ 24\qquad\textbf{(C)}\ 26\qquad\textbf{(D)}\ 30\qquad\textbf{(E)}\ 36 </math> | ||
| + | |||
| + | ==Solution== | ||
| + | Count the number of sides that are not exposed, where a cube is connected to another cube and subtract it from the total number of faces. There are <math>5</math> places with two adjacent cubes, covering <math>10</math> sides, and <math>(6)(6)=36</math> faces. The exposed surface area is <math>36-10 = \boxed{\text{(C)}\ 26}</math>. | ||
| + | |||
| + | ==See Also== | ||
| + | {{AMC8 box|year=2002|num-b=21|num-a=23}} | ||
| + | {{MAA Notice}} | ||
Revision as of 10:37, 5 November 2020
Problem
Six cubes, each an inch on an edge, are fastened together, as shown. Find the total surface area in square inches. Include the top, bottom, and sides.
![[asy] /* AMC8 2002 #22 Problem */ draw((0,0)--(0,1)--(1,1)--(1,0)--cycle); draw((0,1)--(0.5,1.5)--(1.5,1.5)--(1,1)); draw((1,0)--(1.5,0.5)--(1.5,1.5)); draw((0.5,1.5)--(1,2)--(1.5,2)); draw((1.5,1.5)--(1.5,3.5)--(2,4)--(3,4)--(2.5,3.5)--(2.5,0.5)--(1.5,.5)); draw((1.5,3.5)--(2.5,3.5)); draw((1.5,1.5)--(3.5,1.5)--(3.5,2.5)--(1.5,2.5)); draw((3,4)--(3,3)--(2.5,2.5)); draw((3,3)--(4,3)--(4,2)--(3.5,1.5)); draw((4,3)--(3.5,2.5)); draw((2.5,.5)--(3,1)--(3,1.5));[/asy]](http://latex.artofproblemsolving.com/6/5/2/6529094e601d11c16feb8a8834704d6fc4d4cfc0.png)
Solution
Count the number of sides that are not exposed, where a cube is connected to another cube and subtract it from the total number of faces. There are 
places with two adjacent cubes, covering 
sides, and 
faces. The exposed surface area is 
.
See Also
| 2002 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 21 |
Followed by Problem 23 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
