MathDB
1997 AJHSME #21 - Surface Area

Source:

June 30, 2011
geometry3D geometryAMC

Problem Statement

Each corner cube is removed from this 3 cm×3 cm×3 cm3\text{ cm}\times 3\text{ cm}\times 3\text{ cm} cube. The surface area of the remaining figure is
[asy]draw((2.7,3.99)--(0,3)--(0,0)); draw((3.7,3.99)--(1,3)--(1,0)); draw((4.7,3.99)--(2,3)--(2,0)); draw((5.7,3.99)--(3,3)--(3,0));
draw((0,0)--(3,0)--(5.7,0.99)); draw((0,1)--(3,1)--(5.7,1.99)); draw((0,2)--(3,2)--(5.7,2.99)); draw((0,3)--(3,3)--(5.7,3.99));
draw((0,3)--(3,3)--(3,0)); draw((0.9,3.33)--(3.9,3.33)--(3.9,0.33)); draw((1.8,3.66)--(4.8,3.66)--(4.8,0.66)); draw((2.7,3.99)--(5.7,3.99)--(5.7,0.99)); [/asy]
<spanclass=latexbold>(A)</span> 19 sq.cm<spanclass=latexbold>(B)</span> 24 sq.cm<spanclass=latexbold>(C)</span> 30 sq.cm<spanclass=latexbold>(D)</span> 54 sq.cm<spanclass=latexbold>(E)</span> 72 sq.cm<span class='latex-bold'>(A)</span>\ 19\text{ sq.cm} \qquad <span class='latex-bold'>(B)</span>\ 24\text{ sq.cm} \qquad <span class='latex-bold'>(C)</span>\ 30\text{ sq.cm} \qquad <span class='latex-bold'>(D)</span>\ 54\text{ sq.cm} \qquad <span class='latex-bold'>(E)</span>\ 72\text{ sq.cm}