Question

A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges
the two smaller cubes are 6 cm and 8 cm, find the edge of the third smaller cube
11 no 100m 50 mand 18m How many personscans​

Answer 1

$Given \: : Edge \: \: of \: \: melted \: \: cube \: = \bold{12cm }\: \\ and \: \: the \: edges \: \: of \: smaller \: cubes \: are \: = \bold{ 6cm \: \: and \: \: 8cm \: }$

$To \: find \: : \: The \: \: edge \: \: of \: {3}^{rd} cube$

$\large \underline{ \underline{Solution}}$

Let the edge of third cube be x

$\because \: vol \: of \: bigger \: cube \: = \: sum \: of \: vol \: of \: smaller \: cubes$

$\implies \: {12}^{3} = {x}^{3} + {6}^{3} + {8}^{3} \\ \\ \implies \: \: 1728 \: = {x}^{3} + 216 + 512 \\ \\ \implies \: {x}^{3} = 1728 - 216 - 512 \: \\ \\ \implies \: {x}^{3} = 1000 \\ \\ \implies \: x = \sqrt[3]{1000}$

$\implies \: \large{ \bold{ \underline{ \underline{ x \: = \: 10}}}}$

Thus, the edge of third cube is 10cm

Answer 2

Question :-

→ A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges the two smaller cubes are 6 cm and 8 cm, find the edge of the third smaller cube ?

Solution :-

→ 10 cm

Given :-

$\tt{→ Edge \: of \: a \: bigger \: cube \: ( R ) = 12 m } \:$

$\tt{→ Edge \: of \: a \: first \: smaller \: cube \: ( {r}^{2} ) = 8 m }$

$\tt{→ Edge \: of \: a \: second \: smaller \: cube \: ( {r}^{2} ) = 6m }$

$\tt{→ Volume \: of \: a \: cube = {side}^{3}}$

$\tt{→ Volume \: of \: a \: bigger \: cube ( V ) = {sides}^{3}}$

$\tt{= {12}^{3} = {1728}^{3} }$

$\tt{→ It \: is \: melted \: into \: three \: other \: cubes \: , so \: the}$

$\tt{volume \: of \: the \: smaller \: cubes \: remains \: same \: as}$

$\tt{the \: volume \: of \: bigger \: cube . }$

$\tt{→ Volume \: of \: the \: first \: smaller \: cubes ( V1 ) }$

$\tt{→ {8}^{3} = {512m}^{3}}$

$\tt{→ Volume \: of \: second \: smaller \: cube ( V2 ) = {6}^{3} = {216m}^{3} }$

→ Total volume ( V ) = volume of first smaller cube ( V1 ) + volume of second smaller cube ( V2 ) + + volume of third smaller cube ( V3 )

→ V = V1 + V2 + V3

→ 1728 = 512 + 216 + V3

→ 1728 = 728 + V3

→ 1728 - 728 = V3

→ 1000 = V3

$\tt{→ Volume \: of \: third \: cube = {1000m}^{3}}$

$\tt{→ {Edge}^{3} = 1000 }$

$\tt{→ Edge = \sqrt[3]{1000}}$

$\tt{→ Edge = \sqrt[3]{10 \times 10 \times 10}}$

$\boxed{ \tt{→ Edge = 10 m }}$

→Hence , the edge of the third cube is 10m