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 $$S$$.$$\therefore$$ $$({S)}^{3}=216$$$$\Rightarrow$$$$S=6$$ cmRatio 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 $$4:1$$MathematicsRS AgarwalStandard IX

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