Question : The sides of the three cubes of metal are $15 \text{ cm}, 18 \text{ cm}$ and $25 \text{ cm}$, respectively. Find the side (in $\text{cm}$) of the new cube formed by melting these cubes together.
Option 1: $9 \sqrt[3]{388}$
Option 2: $6 \sqrt[3]{388}$
Option 3: $7 \sqrt[3]{388}$
Option 4: $4 \sqrt[3]{388}$
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Correct Answer: $4 \sqrt[3]{388}$
Solution :
Let the side of the new cube be $a\text{ cm}$.
Volume of 1st cube, $V{_1} = 15^3 = 3375\text{ cm}^3$
Volume of 2nd cube, $V{_2} = 18^3 =5832 \text{ cm}^3$
Volume of 3rd cube, $V{_3} = 25^3 = 15625\text{ cm}^3$
$\therefore$ Volume of new cube, $a^3= V{_1}+V{_2}+V{_3}$
$⇒a^3 = 3375+5832+15625 = 24832\text{ cm}^3$
$\therefore a = \sqrt[3]{24832} =4\sqrt[3]{388}\text{ cm}$
Hence, the correct answer is $4\sqrt[3]{388}$.
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