Question

The length, width and height of the given unit cube is divided into 2, 4 and 2 equal parts respectively. Find the volume of the smaller prism so formed.

• A. $\frac{1}{8}\text{cu units}$
• B. $\frac{1}{16}\text{cu units}$
• C. $\frac{1}{32}\text{cu units}$
• D. $\frac{1}{24}\text{cu units}$

Answer 1

The correct option is B $\frac{1}{16}\text{cu units}$

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
$=2\times 4\times 2$
= 16

Volume of one small rectangular prism
$=\frac{\text{Volume of the whole cube}}{\text{Total number of smaller rectangular prism}}$
$=\frac{1}{16}\text{cu units.}$