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Question

A solid cube of side $$12$$ cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.


Solution

Given:
Side $$12$$cm

$$\Rightarrow$$Volume of cube $$=12\times 12\times 12=1728$$cm$$^{3}$$

$$\Rightarrow$$Volume of smaller cube 
$$=\cfrac{1}{8}$$ of $$1728$$
$$=\cfrac{1}{8}\times 1728=216$$cm$$^{3}$$

$$\Rightarrow$$Let side be $$S$$.
$$\therefore$$ $$({S)}^{3}=216$$
$$\Rightarrow$$$$S=6$$ cm

Ratio of SA of cubes 
$$=\cfrac { \text{SA of bigger cube}}{\text{SA of smaller cube} } $$

$$={ \left( \dfrac { 12 }{ 6 }  \right)  }^{ 2 }=\cfrac { { 2 }^{ 2 } }{ 1 } =\cfrac { 4 }{ 1 } $$

$$\therefore$$ Ratio between their surface areas $$4:1$$

Mathematics
RS Agarwal
Standard IX

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