# Difference between revisions of "2017 AMC 10B Problems/Problem 6"

## Problem

What is the largest number of solid $2\text{in}$ by $2\text{in}$ by $1\text{in}$ blocks that can fit in a $3\text{in}$ by $2\text{in}$ by $3\text{in}$ box?

$\textbf{(A)}\ 3\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 7$

## Solution

By simply finding the volume of the larger block, we see that its area is $18$. The volume of the smaller block is $4$. Dividing the two, we see that only a maximum of $4$ $2$in x$2$in x$1$in blocks can fit inside a $3$-in by $2$ in by $3$in box. $\qquad\textbf{(B)}\ 4$

 2017 AMC 10B (Problems • Answer Key • Resources) Preceded byProblem 5 Followed byProblem 7 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 AMC 10 Problems and Solutions