Question

A rectangular prism with a volume of 10 cubic units is filled with cubes with side length of 1/2 unit

Answer 1

We know that:

`1. \space\ V_(Rectangular \space\ prism) = 10 \text\] units^(3)\\\\2. \space\ L_(Small \space\ cube) = (1)/(2) \space\ units\\\\ 3. \space\ V_(Small \space\ cube) = L ^(3)`

Step-1: Find the volume of the small cube.

`V_(Small \space\ cube) = L ^(3)`

`V_(Small \space\ cube) = ((1)/(2)) ^(3)`

`V_(Small \space\ cube) = ((1)/(2)) ((1)/(2)) ((1)/(2))`

`V_(Small \space\ cube) = (1)/(8) \space\ units^(3)`

Step-2: Divide.

`(10)/((1)/(8) )\\\\ \Rrightarrow(10)(8)\\ \\ \Rrightarrow 80`

Hence, 80 cubes can be fit in the rectangular prism.

Answer 2

volume of rectangular prism = 10 units³

volume of each cube =
`(1)/(2) *(1)/(2) *(1)/(2) = (1)/(8) units^3`

required cubes =
`(10)/( (1)/(8) )= 80`