Question

What is the largest number of solid $2$ -in $\times$ $2$ -in $\times$ $1$ -in blocks that can fit in a $3$ -in $\times$ $2$ -in $\times$ $3$ -in box?

$3$

$4$

$5$

$6$

$7$

Answer: B

Concepts:volume rectangular prism bounding to limit cases

Difficulty rating: 1070

Solution:

The volume of the large solid object is $3\cdot 3\cdot 2 = 18$ and volume of the smaller object is $2\cdot 2\cdot 1=4.$ This means we can fit at most $4$ of the small objects.

We can make this happen by putting $3$ of the small objects in a $3 \times 2 \times 2$ rectangular prism, and then we have a $3 \times 2 \times 1$ space left where we can place one small object.

Thus, the correct answer is B .

2017 AMC 10B Problem 6

Answer: B

Difficulty rating: 1070

Solution:

Problem 6 in Other Years