Question

Three cubes having edge 18 cm 24 cm 30 cm respectively are melted and made into a new cube find the edge of the new cube so formed






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Answer 1

Answer:-

Your Answer Is 36 cm.

Explanation:-

Given:-

• Edges of three cubes = 18cm, 24cm and 30cm.

• All three cubes are melted to made a new cube.

To Find:-

• The edge of new cube formed.

Formula Used:-

↦ Volume of cube = $\tt edge^3$

Solution:-

Let the edge of bigger cube be x.

Since Three cubes are melted to make a bigger cube and therefore,

↦ Total Volume of 3 cubes = Volume of bigger cube.

$\tt \mapsto {18}^{3} + {24}^{3} + 30 {}^{3} = {x}^{3} .$

$\\ \tt \mapsto 5832 + 13824 + 27000 = {x}^{3} .$

$\\ \tt \mapsto {x}^{3} = 46656.$

$\\ \tt \mapsto x = \sqrt[3]{46656} .$

$\\ \large \red{\bf \mapsto { \underline{ \boxed{ \blue{ \underline{ \bf x = 36}}}}}}$

Therefore The Edge Of the Cube Is 36 cm.

Answer 2

Question:-

• Three cubes having edge 18 cm 24 cm 30 cm respectively are melted and made into a new cube find the edge of the new cube so formed.

To Find:-

• Find the edge of the new cube formed.

Solution:-

• Edge of three cubes = 18 cm , 24 cm , 30 cm.

• All cubes are melted and made into a new cube.

• Let the volume of new cube be x

We have to find the edge of the new cube formed:-

$\dashrightarrow\sf \: Total \: volume \: of \: all \: cubes = Volume \: of \: a \: new \: cube$

$\dashrightarrow\sf \: { ( 18 ) }^{ 3 } + { ( 24 ) }^{ 3 } + { ( 30 ) }^{ 3 } = { ( x ) }^{ 3 }$

$\dashrightarrow\sf \: { ( x ) }^{ 3 } = 5832 + 13824 + 27000$

$\dashrightarrow\sf \: { ( x ) }^{ 3 } = 46656$

$\dashrightarrow\sf \: x = { 46656 }^{ 1/3 }$

$\dashrightarrow\sf \: x = { ( 36 ) }^{ 3 \times \frac { 1 } { 3 } }$

$\dashrightarrow\sf \: x = 36$

Hence ,

• Edge of cube is 36 cm.