Question

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A rectangular prism is completely packed with 90 cubes of edge length fraction 1 over 2 inch, without any gap or overlap. Which of the following describes the volume of this rectangular prism?

11 unit cubes and 1 smaller cube of volume fraction 1 over 8 cubic inch

22 unit cubes and 4 smaller cubes of volume fraction 1 over 8 cubic inch each

11 unit cubes and 2 smaller cubes of volume fraction 1 over 8 cubic inch each

22 unit cubes and 2 smaller cubes of volume fraction 1 over 8 cubic inch each

Answer 1

The volume of each those small cubes is \[\large V = (\frac{ 1 }{ 2 })^3 = \frac{ 1 }{ 8 }\]

Answer 2

90 of those will have a total volume for the prism of; 90/8

Answer 3

A "unit cube" is just a volume of 1 each...

The total Prism volume of 90/8 = 11 + 2/8

Answer 4

You would need 11 unit cubes and 2 of those small cubes , to total 90/8