Question

See metallic cubic those edges are 3 cm, 4cm, and 5cm are melted and recast into a single cube find the edge of a cube to form. ​

Answer 1

$Let \:a = 3 \:cm, b = 4 \:cm \:and \: c = 5 \:cm \\are \: edges \:of \:three \: cubes$

/* According to the problem given */

If these three cubes are melted and recast into a single cube then

$Let \:edge \:of \:a \:single \:cube = d \:cm$

$V_{(single \:cube )} \\= Sum \:of \:the \: volumes of \: three \:cubes$

$\implies d^{3} = a^{3} + b^{3} + c^{3} \\= 3^{3} + 4^{3} + 5^{3}\\= 27 + 64 + 125 \\ = 216$

$\implies d^{3} = 6^{3}$

$\implies d = 6 \:cm$

Therefore.,

$\red {Edge \:of \:a \:single \:cube}\green {= 6 \:cm}$

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