Question

How many cubes with side lengths of \dfrac13\text{ cm} 3 1 ​ cmstart fraction, 1, divided by, 3, end fraction, start text, space, c, m, end text does it take to fill the prism?

Answer 1

Answer:

48 cubes

Explanation:

Given

Cube

$Side\ Length = \frac{1}{3}cm$

Prism [Missing from the question]

$Length = 1cm$

$Width= 2\frac{2}{3}cm$

$Height = \frac{2}{3}cm$

Required

Determine the number of cubes the prism can take

Volume is calculated as:

$V = Length * Width * Height$

First, calculate the volume of the cube

$V_1 = \frac{1}{3} * \frac{1}{3} * \frac{1}{3} cm^3$

$V_1 = \frac{1}{27} cm^3$

Next, calculate the volume of the prism

$V_2 = 1 * 2\frac{2}{3} * \frac{2}{3}\ cm^3$

Convert to improper fraction

$V_2 = 1 * \frac{8}{3} * \frac{2}{3}\ cm^3$

$V_2 = \frac{16}{9}\ cm^3$

Divide V2 by V1 to get the number of cubes

$Number = \frac{V_2}{V_1}$

$Number = \frac{16}{9}/\frac{1}{27}$

$Number = \frac{16}{9}*\frac{27}{1}$

$Number = \frac{16*27}{9*1}$

$Number = \frac{432}{9}$

$Number = 48$

Hence, 48 cubes will fill the prism

Answer 2

Answer: 48 cubes.

Explanation:

V=H*L*W

3*8*2

This equals 48.