MathDB

11

Part of 2008 AMC 12/AHSME

Problems(2)

Cube Stacking

Source: AMC 12 2008A Problem 11

2/17/2008
Three cubes are each formed from the pattern shown. They are then stacked on a table one on top of another so that the 13 13 visible numbers have the greatest possible sum. What is that sum? [asy]unitsize(.8cm);
pen p = linewidth(.8pt); draw(shift(-2,0)*unitsquare,p); label("1",(-1.5,0.5)); draw(shift(-1,0)*unitsquare,p); label("2",(-0.5,0.5)); label("32",(0.5,0.5)); draw(shift(1,0)*unitsquare,p); label("16",(1.5,0.5)); draw(shift(0,1)*unitsquare,p); label("4",(0.5,1.5)); draw(shift(0,-1)*unitsquare,p); label("8",(0.5,-0.5));[/asy]<spanclass=′latex−bold′>(A)</span> 154<spanclass=′latex−bold′>(B)</span> 159<spanclass=′latex−bold′>(C)</span> 164<spanclass=′latex−bold′>(D)</span> 167<spanclass=′latex−bold′>(E)</span> 189 <span class='latex-bold'>(A)</span>\ 154 \qquad <span class='latex-bold'>(B)</span>\ 159 \qquad <span class='latex-bold'>(C)</span>\ 164 \qquad <span class='latex-bold'>(D)</span>\ 167 \qquad <span class='latex-bold'>(E)</span>\ 189
geometry3D geometryAMC
Ocean Floor Mountain

Source: AMC 12 2008B Problem 11

2/29/2008
A cone-shaped mountain has its base on the ocean floor and has a height of 8000 8000 feet. The top 18 \frac{1}{8} of the volume of the mountain is above water. What is the depth of the ocean at the base of the mountain, in feet? (A)\ 4000 \qquad (B)\ 2000(4\minus{}\sqrt{2}) \qquad (C)\ 6000 \qquad (D)\ 6400 \qquad (E)\ 7000
geometry3D geometryAMC