Question

Three metallic solid cubes with edges of length 3cm, 4cm and 5cm respectively are melted and recast into a new solid cube.

Find (1) volume and (2) surface area of new cube

please provide a step by step explanation
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Answer 1

$\huge{ \underbrace{ \text{Question}}}$

Three metallic solid cubes with edges of length 3cm, 4cm and 5cm respectively are melted and recast into a new solid cube.

Find :-

• (1) volume and
• (2) surface area of new cube

$\huge{ \underbrace{ \text{Answer}}}$

Given:-

Three metallic solid cubes with edges of length 3cm, 4cm and 5cm which are melted and recast to a new solid cube.

To Find:-

$\rm{ \rightarrow{Volume \: of \: the \: new \: solid \: cube}} \\ \\ \rm{ \rightarrow{Surface \: area \: of \: the \: new \: solid \: cube}}$

Solution:-

We know that,

$\boxed{ \underline{ \rm{ \blue{ \bold{Volume \: of \: a \: cube }= {a}^{3} }}}}$

First, let's find the volume of each cubes-

$\sf{ \implies{Volume \: of \: the \: 1st \: cube = {(3cm)}^{3} = 27 {cm}^{3} }} \\ \\ \sf{ \implies{Volume \: of \: the \: 2nd \: cube = {(4cm)}^{3} = 64 {cm}^{3} }} \\ \\ \sf{ \implies{Volume \: of \: the \: 3rd\: cube = {(5cm)}^{3} = 125 {cm}^{3} }}$

Now,

$\sf{ \rightarrow{Total \: voume \: of \: the \: cubes = (27 + 64 + 125) {cm}^{3} }} \\ \\ \sf{ \therefore{Total \: voume \: of \: the \: cubes = \orange{216 {cm}^{3} }}}$

Therefore,

$\sf\rightarrow{{Edge \: of \: cube = \sqrt[3]{216}cm = \bold{6cm}}}$

Again,

We know that,

$\boxed{ \underline{ \rm{ \blue{ \bold{Surface \: area \: of \: a \: cube} = 6 {a}^{2} }}}}$

According to the question,

$\sf{ \implies{Surface \: area \: of \: the \: cube = 6 {(6cm)}^{2} }} \\ \\ \sf{ \implies{surface \: area \: of \: the \: cube = (6 \times 12 )cm {}^{2} }} \\ \\ \sf{ \implies{surface \: area \: of \: the \: cube = \orange{216cm {}^{2} } }}$

$\underline{ \boxed{ \rm{Hence, \: area \: of \: the \: new \: solid \: cube \: is \: 216 {cm}^{3} }}}$

$\underline{ \boxed{ \rm{And \: surface \: area \: of \: the \: new \: solid \: cube \: is \: 216 {cm}^{2} }}}$

Answer 2

Step-by-step explanation:

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