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There are three glass cubes of edges $20 \mathrm{~cm}, 16 \mathrm{~cm}$ and $12 \mathrm{~cm}$ respectively. These are melted to form a new cube. Find the edge of the new cube.

(a) $26 \mathrm{~cm}$

(b) $28 \mathrm{~cm}$

(c) $24 \mathrm{~cm}$

(d) $22 \mathrm{~cm}$

Solution :

The sum of the volumes of

three cubes $=(20)^{3}+(16)^{3}+(12)^{3}$

$=8000+4096+1728$

$=13824 \mathrm{~cm}^{3}$

$\therefore$ Edge of the new cube

$$\begin{array}{l} =\sqrt[3]{13824} \\ =24 \mathrm{~cm} ; \text { Ans. } \end{array}$$

$\therefore$ Correct option $is(c)$

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