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Volume and Surface area of Solids — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsVolume and Surface area of Solids3 Marks
Question
Three metallic cubes whose edges are $3\ cm, 4\ cm$ and $5\ cm$, are melted and recast into a single large cube. Find the edge of the new cube formed.
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Answer

We have,
Edges of the cubes : $a_1 = 3cm, a_2 = 4cm$ nnd $a_3 = 5cm$
Let the edge of the new cube be a.
Now
Volume of the new cube $=\text{a}_1^3+\text{a}_2^3+\text{a}_3^2$
$\Rightarrow\text{a}^3=3^3+4^3+5^3$
$\Rightarrow\text{a}^3=27+64+125$
$\Rightarrow\text{a}^3={216}$
$\Rightarrow\text{a}=\sqrt[3]{216}$
$\therefore\text{a}=6\text{cm}$
so, the edge of the new cube so formed is $6\ cm$.

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