Question

A rectangular prism with a volume of 4 cubic units is filled with cubes with side lengths of 1/3 unit. How many 1/3 unit cubes does it take to fill the prism?
Please answer quickly, thanks!

Answer 1

Answer:

108

Step-by-step explanation:

Volume of small cube:

• 1/3*1/3*1/3= 1/27 cubic unit

1 cubic unit volume will fit

• 1÷1/27= 27 small cubes

4 cubic unit volume will fit:

• 4*27= 108 small cubes

Answer: 108 small cubes will fill the prism

Answer 2

We need to recall the following formulas of the volume.

• The volume of a cuboid $=length\times Width\times Height$
• The volume of a cube $=(Length)^3$

This problem is about the volume.

Given:

The volume of a rectangular prism $=4$ cubic units

The prism is filled with cubes with side lengths of $\frac{1}{3}$ units.

Let's consider,

The prism is filled with $N$ numbers of cubes with side lengths of $\frac{1}{3}$ units.

Then,

Volume of a prism $=N\times$ Volume of a cube

$4=N\times (\frac{1}{3})^3$

$4=N\times(\frac{1}{27} )$

$N=4\times 27$

$N=108$

Hence, $108$ cubes are required to fill the prism.