Question

three metal cubes of sides 5 cm 4 cm and 3 cm are melted and recast into a new cube find the edge of the new cube of formed.​

Answer 1

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

• three metal cubes of sides 5 cm 4 cm and 3 cm are melted and recast into a new cube find the edge of the new cube of formed.

$\large\underline{ \underline{ \sf \maltese{ \: Solution:- }}}$

$\underbrace\red{\boxed{ \sf \blue{ Volume \: of \: the \: First\: Cube }}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Volume \: of \: the \: first \: cube \: = \: (side)^{3} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Volume \: of \: the \: first \: cube \: = \: (5cm)^{3} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Volume \: of \: the \: first \: cube \: = \: 5 \times 5 \times 5 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Volume \: of \: the \: first \: cube \: = \: 125cm^{3} }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{Volume \: of \: first \: Cube\: = \: 125cm^{3} }}}$

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$\underbrace\red{\boxed{ \sf \blue{ Volume \: of \: the \: Second \: Cube }}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Volume \: of \: the \: Second \: cube \: = \: (side)^{3} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Volume \: of \: the \: first \: cube \: = \: (4cm)^{3} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Volume \: of \: the \: first \: cube \: = \: 4 \times 4 \times 4 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Volume \: of \: the \: first \: cube \: = \: 64cm^{3} }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{Volume \: of \: first \: Cube\: = \: 64cm^{3} }}}$

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$\underbrace\red{\boxed{ \sf \blue{ Volume \: of \: the \: Third \: Cube }}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Volume \: of \: the \: Third \: cube \: = \: (side)^{3} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Volume \: of \: the \: first \: cube \: = \: (3cm)^{3} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Volume \: of \: the \: first \: cube \: = \: 3 \times 3 \times 3 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Volume \: of \: the \: first \: cube \: = \: 27cm^{3} }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{Volume \: of \: first \: Cube\: = \: 27cm^{3} }}}$

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Since the new cube is made from all the three cubes, So the volume of the new cube will be the sum of the Volumes of all the three cubes.

$\underbrace\red{\boxed{ \sf \blue{ Volume \: of \: the \: New\: Cube }}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Volume \: of \: the \: New \: cube \: = \: ( \: 125 \: + \: 64 \: + \: 27 \: ) \: cm ^{3} }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{Volume \: of \: New \: Cube\: = \: 216cm^{3} }}}$

$\underbrace\red{\boxed{ \sf \blue{ Edge \: of \: the \: New \: Cube\: Formed }}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ {(side)}^{3} \: = \: 216 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ Side \: = \: \sqrt[3]{216} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Side \: = \: 6 \times \: 6 \times \: 6 \: }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{Side \: = \: 6cm }}}$

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$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Edge \: of \: the \: New \: Cube \: = \underline {\underline{ 6cm}}}\\\end{gathered}\end{gathered}$

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