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

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Solution

## 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, ${V}_{1}={a}_{1}^{3}\phantom{\rule{0ex}{0ex}}\frac{1}{8}={a}_{1}^{3}\phantom{\rule{0ex}{0ex}}{a}_{1}=\sqrt[3]{\frac{1}{8}}\phantom{\rule{0ex}{0ex}}{a}_{1}=\frac{1}{2}$So, the side of the first cube is $\frac{1}{2}=0.5cm$Similarly, ${V}_{2}=1$${V}_{2}={a}_{2}^{3}\phantom{\rule{0ex}{0ex}}1={a}_{2}^{3}\phantom{\rule{0ex}{0ex}}{a}_{2}=\sqrt[3]{1}\phantom{\rule{0ex}{0ex}}{a}_{2}=1$ and ${V}_{3}={a}_{3}^{3}\phantom{\rule{0ex}{0ex}}8={a}_{3}^{3}\phantom{\rule{0ex}{0ex}}{a}_{3}=\sqrt[3]{8}\phantom{\rule{0ex}{0ex}}{a}_{3}=2$So, ${a}_{2}=1cmand{a}_{3}=2cm$Therefore, the total height of the staked cube = ${a}_{1}+{a}_{2}+{a}_{3}=0.5+1+2=3.5cm$.

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