Question

three solid cubes of edges 8cm,xcm and x10 cm are melted and recast into single cube of side 12 cm find x
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Answer 1

Given :-

Three solid cubes of edges 8 cm , X cm and 10 cm are melted and recast into a single cube of side 12 cm.

To find :-

The value of X

Solution :-

Given that

The edges of the three cubes are 8 cm , X cm and 10 cm

Given that

The three cubes are melted and recast into a single cube then the sum of all the volumes of the cubes is equal to the volume of the resultant cube

The edge of the resultant cube = 12 cm

We know that

Volume of a cube whose edge is a units is 'a³' Cubic units

Volume of the cube whose edge is 8 cm

= 8³ = 8×8×8 = 512 cm³

Volume of the cube whose edge is X cm

= X³ cm³

Volume of the cube whose edge is 10 cm

= 10³ = 10×10×10 = 1000 cm³

Volume of the resultant cube whose edge is

12 cm = 12³ = 12×12×12 = 1728 cm³

Therefore,

The sum of the three volumes of the cubes

= The volume of the resultant cube

=> 512 + X³ + 1000 = 1728

=> X³+1512 = 1728

=> X³ = 1728-1512

=> X³ = 216

=> X³ = 6³

On comparing both sides then

X = 6 cm

Therefore, X = 6 cm

Answer :-

The value of X is 6 cm

Used formulae:-

• Volume of a cube whose edge is a units is 'a³' Cubic units

Used Concept :-

• If some solids are melted and recast a new solid then the sum of all the volumes of the solids is equal to the volume of the resultant solid.

Answer 2

$\star \; {\underline{\boxed{\color{darkblue}{\pmb{\frak{ \; Given \; :- }}}}}}$

• Side of 1st Cube = 8 cm
• Side of 2nd Cube = x cm
• Side of 3rd Cube = 10 cm
• Side of New Cube = 12 cm

$\star \; {\underline{\boxed{\pink{\pmb{\frak{ \; To \; Find \; :- }}}}}}$

• Find the Value of x

$\\ \qquad{\rule{200pt}{2pt}}$

$\star \; {\underline{\boxed{\red{\pmb{\frak{ \; SolutioN \; :- }}}}}}$

$\dag$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Volume{\small_{(Cube)}} = {Edge}^{3} }}}}}$

$\maltese$ Calculating the Value of x :

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { Volume_1 + Volume_2 + Volume_3 = Volume{\small_{(New \; Cube)}} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { {Side}^{3} + {Side}^{3} + {Side}^{3} = {Side}^{3} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { {8}^{3} + {x}^{3} + {10}^{3} = {12}^{3} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 512 + {x}^{3} + 1000 = 1728 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { {x}^{3} + 1512 = 1728 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { {x}^{3} = 1728 - 1512 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { {x}^{3} = 216 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { x = \sqrt{216} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; {\underline{\boxed{\pmb{\sf{ x = 6 }}}}} \; {\pmb{\purple{\bigstar}}} \\ \\ \\ \end{gathered}$

$\therefore \;$ Value of x is 6 cm .

$\\ \qquad{\rule{200pt}{2pt}}$