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Question
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.
Solution
\[\text { We have the following: } \]
\[\text { Length of the edge of cube A = 18 cm }\]
\[\text { Length of the edge of cube B = 24 cm }\]
\[\text { Length of the edge of cube C = 30 cm }\]
\[\text { The given cubes are melted and moulded into a new cube D }. \]
\[\text { Hence, volume of cube D = volume of cube A + volume of cube B + volume of cube C }\]
\[ =\text { (side of cube A ) }^3 + \text { (side of cube B })^3 + \text { (side of cube C })^3 \]
\[ = {18}^3 + {24}^3 + {30}^3 \]
\[ = 5832 + 13824 + 27000\]
\[ = 46656 {cm}^3 \]
\[\text { Suppose that the edge of the new cube D = x }\]
\[ \Rightarrow x^3 = 46656\]
\[ \Rightarrow x = \sqrt[3]{46656} = 36 cm\]
\[ \therefore \text { The edge of the bigger cube D is 36 } cm .\]
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