Question

Three cubes of metal of sides 6 cm, 8 cm and 10 cm are melted and made into a single cube. Find the edge of the new cube.

Answer 1

Answer:

$\red { Edge \: of \:new \:cube } \green {= 12\:cm }$

Step-by-step explanation:

$Let \: a ,b \:and c \: are \: sides \: of \: three\\ cubes \: respectively$

$a = 6\:cm , \: b = 8\:cm ,\:and \:c = 10\:cm$

/* According to the problem given,

If three metal cubes melted and made into a single cube

$Side \: of \: new \:cube = S$

$Volume \: of \:a \: new \:cube \\=sum \:of \: volumes \:of \: three \:cubes$

$\boxed { \pink { Volume \:of \:a \:cube = (side)^{3}}}$

$S^{3} = a^{3} + b^{3} + c^{3}\\=6^{3} + 8^{3} + 10^{3}\\= 216 + 512 + 1000\\= 1728$

$\implies S^{3} = (12)^{3}$

$\implies S = 12 \:cm$

Therefore.,

$\red { Edge \: of \:new \:cube } \green {= 12\:cm }$

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Answer 2

Question :Three cubes of metal of edge 6 cm, 8 cm and 10 cm are melted and made into a single cube. Find the edge of the new cube.

Solution :

$\underline{\bold {Given:}}$

• The edges of three cubes are 6 cm, 8cm and 10 cm.

$\underline{\bold {To\:Find}}$

• The edge of the new cube .

Let the edges of three cubes be A=6 cm,B=8 cm and C= 10 cm

Let the edge of new cube be S.

$\boxed{\blue{Volume \:of\:cube=(Edge)^3}}$

• Volume of edge of new cube = Sum of volume of edges of three cubes because we have to made three cubes into a single cube .

$= > Volume\: of \:S = Sum\: of volume\: of\: A,\:B \:and\:C .\\= > {S}^{3} = {A}^{3} + {B}^{3} + {C}^{3} \\ = > {S}^{3} = {6}^{3} + {8}^{3} + {10}^{3} \\ = > {S}^{3} = 216 + 512 + 1000 \\ = > {S}^{3} = 1728 \\ = > S = \sqrt[3]{1728} \\ = > S = \sqrt[3]{12 \times 12 \times 12} \\ = > S = 12$

$\fbox{\green {Edge\:of\:new\:cube=12\:cm}}$

$\bold {Hence, Edge \:of \:new\: cube = 12\:cm}$

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