Small cubes with edge lengths of 1/4 inch will be packed into a rectangular prism (shown below). How many small cubes are needed to completely fill the rectangular prism?

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Thank you for the answer!

2 Answers
Jan 6, 2018

it's a volume question

Explanation:

First, find the volume of the small shape. ( 1/4 times 1/4 times 1/4) = 1/64

Then, divide the volume of the bigger shape. (4.1/2 times 5 times 3.3/4) = 675/8

Finally, divide the big shape volume by the small shape volume. (675/8 divide 1/64)= 5400

Smaller shapes will fit into bigger shapes.

Jan 6, 2018

5400

Explanation:

Using a word incorrectly for mathematics; it is a matter of how many 'towers' of 1/4inch blocks you can fit it.

Consider the height of one 'tower'

Height ->3 3/4" inches "-> 15/4

color(brown)("So for the height we have 15 blocks")

Consider the 5 inches depth ->20/4

color(brown)("So for the depth we have 20 'towers'")

Consider the 4 1/2 width ->18/4

color(brown)("So for the width we have 18 'towers'")

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One approach for working it out without a calculator.
Using a calculator is much easier.

Note that 20 is the same as 10xx2 Multiplying by 10 is easy and doubling is straight forward. Taking advantage of this we have:

Total count of 'towers' ->18xx20 = 18xx10xx2 = 360

color(white)()
color(white)()

Total count of blocks at 15 per 'tower' ->15xx360 = 5400

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What follows is just a way of thinking!

color(white)("ddddd") 15color(white)("d")->color(white)("d")[10color(white)("dv")color(white)("dd")+color(white)("dddd")5color(white)("ddd"2/2)]

color(white)("ddddd")15color(white)("d")->color(white)("d")[10color(white)("dd")color(white)("dd")+ color(white)("d") (1/2xx10)]

360xx15->360[10color(white)(/"d")color(white)("d.")+color(white)("d")(1/2xx10)]

360xx15 ->[10xx360]+[1/2xx10xx360]

color(white)("d")

(10xx360)color(white)("dd.")=3600
1/2xx10xx360=ul(1800 larr" Add"
color(white)("dddddddddddddd")5400