Question

A cube whose volume is $\frac{1}{8}$ cubic centimetre is placed on top of a cube whose volume is $1c{m}^3$. The two cubes are then placed on top of a third cube whose volume is $8c{m}^3$. The height of stacked cubes is

Answer 1

Finding the height of stacked cubes:

Let the volume of the cubes be $V_1,V_2,V_3$ whose sides are $a_1,a_2,a_3$ respectively.

We know that,

Volume of the cube$=a^3$

Now, $V_1=\frac{1}{8}$

Therefore,

$$\begin{gathered} V_1=a_1^3 \\ \frac{1}{8}=a_1^3 \\ {a}_1=\sqrt[3]{\frac{1}{8}} \\ {a}_1=\frac{1}{2} \end{gathered}$$

So, the side of the first cube is $\frac{1}{2}=0.5cm$

Similarly,

$V_2=1$

$$\begin{gathered} V_2=a_2^3 \\ 1=a_2^3 \\ {a}_2=\sqrt[3]{1} \\ {a}_2=1 \end{gathered}$$ and $$\begin{gathered} V_3=a_3^3 \\ 8=a_3^3 \\ {a}_3=\sqrt[3]{8} \\ {a}_3=2 \end{gathered}$$

So, $a_2=1cmand{a}_3=2cm$

Therefore, the total height of the staked cube = $a_1+a_2+a_3=0.5+1+2=3.5cm$.