Question

A unit cube is divided into equal parts as shown below. The volume of each smaller prism is cu unit.

• A. $\frac{1}{24}$
• B. $\frac{1}{16}$
• C. $\frac{1}{32}$
• D. $\frac{1}{32}$

Answer 1

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

Given the dimensions of the unit cube:
Length = 1 unit
Width = 1 unit
And height = 1 unit

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

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