Chapter 0.1, Problem 3E

To determine

To calculate:what is the largest cube she could build with the sugar cubes.

Answer to Problem 3E

The largest cube she could build with the sugar cubes $=10.6265a\equiv 11a$

Explanation of Solution

Given information: Megan has 1200 sugar cube.

Suppose the side length of single sugar cube is equal to ‘a’ and the volume of the cubes is equal to ‘V’.

Formula used: Volume of cube (V) = ${\left(\text{Sides}\right)}^3$

Therefore, $V=1200a^3\mathrm{...}\left(\text{i}\right)$

As per the question she made a large cube by using all the 1200 cubes.

Hence, suppose side length of the largest cube is equal to $a`$ and the volume of the large cube is equal to $V`$

Now, $V`=V=a{`}^3\mathrm{...}\left(\text{ii}\right)$

Calculation:

From the equation (i) and (ii), we get

  $\begin{array}{l}\Rightarrow a{`}^3=a^3\\ \Rightarrow a{`}^3=1200a\\ \Rightarrow a`=\sqrt[3]{1200a}=10.6265a\simeq 11a\end{array}$

Therefore, length of the largest cube $=11a$