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# What is the maximum number of 4x4x4 cubes that can fit in a rectangula

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Re: What is the maximum number of 4x4x4 cubes that can fit in a rectangula [#permalink]
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Bunuel wrote:
What is the maximum number of 4x4x4 cubes that can fit in a rectangular box measuring 10x12x16 ?

A. 12
B. 18
C. 20
D. 24
E. 30

M23-06

Official Solution:

What is the maximum number of 4x4x4 cubes that can fit in a rectangular box measuring 10x12x16 ?

A. 12
B. 18
C. 20
D. 24
E. 30

To determine the maximum number of 4x4x4 cubes that can fit in a rectangular box measuring 10x12x16, we must first calculate how many of these smaller cubes can fit in each dimension.

In the length dimension, we can fit a maximum of 10/4 = 2.5 cubes, but since we cannot cut the cubes, we must round down to the nearest whole number, which gives us 2 cubes.

In the width dimension, we can fit a maximum of 12/4 = 3 cubes.

In the height dimension, we can fit a maximum of 16/4 = 4 cubes.

Therefore, the maximum number of 4x4x4 cubes that can fit in the rectangular box is the product of the number of cubes that fit in each dimension, which is 2*3*4 = 24 cubes.

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Re: What is the maximum number of 4x4x4 cubes that can fit in a rectangula [#permalink]
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Re: What is the maximum number of 4x4x4 cubes that can fit in a rectangula [#permalink]
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