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.
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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) $22 \mathrm{~cm}$
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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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