Question

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

Answer 1

volume of rectangular prism = 10 units³

volume of each cube = $\frac{1}{2} \times\frac{1}{2} \times\frac{1}{2} = \frac{1}{8} units^3$

required cubes = $\frac{10}{ \frac{1}{8} }= 80$

Answer 2

Solution:

We know that:

$1. \space\ V_{Rectangular \space\ prism} = 10 \text\] units^{3}\\\\2. \space\ L_{Small \space\ cube} = \frac{1}{2} \space\ units\\\\ 3. \space\ V_{Small \space\ cube} = L ^{3}$

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

$V_{Small \space\ cube} = L ^{3}$

$V_{Small \space\ cube} = (\frac{1}{2}) ^{3}$

$V_{Small \space\ cube} = (\frac{1}{2}) (\frac{1}{2}) (\frac{1}{2})$

$V_{Small \space\ cube} = \frac{1}{8} \space\ units^{3}$

Step-2: Divide.

$\frac{10}{\frac{1}{8} }\\\\ \Rrightarrow(10)(8)\\ \\ \Rrightarrow 80$

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