Cubes A, B, C 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.
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 $36 \mathrm{~cm}$