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

Question

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) $22 \mathrm{~cm}$

Answer 1

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).