Cubes A, B, C having edges 18 cm,
Question:

Cubes ABC having edges 18 cm, 24 cm and 30 cm respectively are melted and moulded into a new cube D. Find the edge of the bigger cube D.

Solution:

We have the following:

Length of the edge of cube $\mathrm{A}=18 \mathrm{~cm}$

Length of the edge of cube $\mathrm{B}=24 \mathrm{~cm}$

Length of the edge of cube $\mathrm{C}=30 \mathrm{~cm}$

The given cubes are melted and moulded into a new cube $\mathrm{D}$.

Hence, volume of cube $\mathrm{D}=$ volume of cube $\mathrm{A}+$ volume of cube $\mathrm{B}+$ volume of cube $\mathrm{C}$

$=(\text { side of cube } \mathrm{A})^{3}+(\text { side of cube } \mathrm{B})^{3}+(\text { side of cube } \mathrm{C})^{3}$

$=18^{3}+24^{3}+30^{3}$

$=5832+13824+27000$

$=46656 \mathrm{~cm}^{3}$

Suppose that the edge of the new cube $\mathrm{D}=\mathrm{x}$

$\Rightarrow \mathrm{x}^{3}=46656$

$\Rightarrow \mathrm{x}=\sqrt[3]{46656}=36 \mathrm{~cm}$

$\therefore$ The edge of the bigger cube $\mathrm{D}$ is $36 \mathrm{~cm}$

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