MathDB
Packing Station

Source: November 2021 AMC 10 A #3

November 11, 2021
AMC 10

Problem Statement

What is the maximum number of balls of clay of radius 22 that can completely fit inside a cube of side length 66 assuming the balls can be reshaped but not compressed before they are packed in the cube?
<spanclass=latexbold>(A)</span>3<spanclass=latexbold>(B)</span>4<spanclass=latexbold>(C)</span>5<spanclass=latexbold>(D)</span>6<spanclass=latexbold>(E)</span>7<span class='latex-bold'>(A) </span>3\qquad<span class='latex-bold'>(B) </span>4\qquad<span class='latex-bold'>(C) </span>5\qquad<span class='latex-bold'>(D) </span>6\qquad<span class='latex-bold'>(E) </span>7