Difference between revisions of "1982 AHSME Problems/Problem 16"
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| − | == Solution | + | ==Problem== |
| + | A wooden cube has edges of length <math>3</math> meters. Square holes, of side one meter, centered in each face are cut through to the opposite face. The edges of the holes are parallel to the edges of the cube. The entire surface area including the inside, in square meters, is | ||
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| + | <math>\text {(A)} 54 \qquad \text {(B)} 72 \qquad \text {(C)} 76 \qquad \text {(D)} 84\qquad \text {(E)} 86</math> | ||
| + | == Solution == | ||
Each exterior unit square which is removed exposes 4 faces of the unit interior squares, so the entire surface area in square meters is <math>6 \cdot 3^2 - 6 + 24=72.</math> | Each exterior unit square which is removed exposes 4 faces of the unit interior squares, so the entire surface area in square meters is <math>6 \cdot 3^2 - 6 + 24=72.</math> | ||
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| + | ==See Also== | ||
| + | {{AHSME box|year=1982|num-b=15|num-a=17}} | ||
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| + | {{MAA Notice}} | ||
Latest revision as of 23:34, 29 June 2025
Problem
A wooden cube has edges of length 
meters. Square holes, of side one meter, centered in each face are cut through to the opposite face. The edges of the holes are parallel to the edges of the cube. The entire surface area including the inside, in square meters, is
Solution
Each exterior unit square which is removed exposes 4 faces of the unit interior squares, so the entire surface area in square meters is 
See Also
| 1982 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 15 |
Followed by Problem 17 | |
| 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 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
