Question

Each of the dimensions of a unit cube is divided into 2 parts. The volume of each of the smaller prism is cu unit.

• A. $\frac{1}{8}$
• B. $\frac{1}{12}$
• C. $\frac{1}{16}$
• D. $\frac{1}{32}$

Answer 1

The correct option is A $\frac{1}{8}$

Given the dimensions of the unit cube:

Length = 1 unit
Width = 1 unit
And height = 1 unit

Therefore,
Volume of the given unit cube
$=\text{length}\times \text{width}\times \text{height}$
$=1\times 1\times 1\text{cu units}$
$=1\text{cu units}$

The smaller rectangular prism looks like:


So,
Total number of smaller rectangular prisms = Number of smaller rectangular prisms in base layer × Number of layers
$=2\times 2\times 2$
= 8

Volume of one small rectangular prism
$=\frac{\text{Volume of the whole cube}}{\text{Total number of smaller rectangular prism}}$
$=\frac{1}{8}\text{cu units.}$