Question

a cubiod is made of metal it is 27cm×18cm×12cm.it is melted and recast into small cubes with an edge 6cm in length.how many such identical cubes are made assuming that there is no wastage in the process ​

Answer 1

$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: SOLUTION \: \: \red{ \mid}}}}}}}}$

$\underline{ \bold{ \: \: GIVEN \: \: }} \\ \\ \bold{Measures \: \: of \: \: the \: \: cuboid = 27 \: cm \times 18 \: cm\times 12 \: cm} \\ \\ \bold{So,} \\ \\ \bold{Length \: \: of \: \: the \: \: cuboid \: ,\: l = 27 \: \: cm} \\ \\ \bold{Breadth \: \: of \: \: cuboid \:, \: b = 18 \: \: cm} \\ \\ \bold{Height \: of \: \: the \: \: cuboid \: ,\: h = 12 \: \: cm}$

$\bold{Thus,} \\ \\ \bold{Volume \: \: of \: \: \: the \: \: cuboid = l \times b \times h} \\ \\ \bold{ = (27 \times 18 \times 12) \: \: cu.cm} \\ \\ \bold{ = 5832 \: \: cu.cm}$



$\bold{Again,} \\ \\ \bold{Length \: \: of \: \: the \: \: edge \: \: of \: \: the \: cube \: \: a = 6 \: \: cm} \\ \\ \bold{Thus,} \\ \\ \bold{Volume \: \: of \: \: the \: \: cube = a {}^{3} } \\ \\ \bold{ =( 6) {}^{3} \: \: cu.cm } \\ \\ \bold{ = 216 \: \: cu.cm}$



$\bold{Now,} \\ \\ \bold{The \: \: number \: \: of \: \: such \: \: cube \: metled \: \: from} \\ \bold{the \: \: cuboid = \frac{Volume \: \: of \: \: cuboid}{Volume \: \: of \: \: \: each \: \: cube} } \\ \\ \bold{ = \frac{5832 \: \: cu.cm}{216 \: \: cu.cm} } \\ \\ \bold{ = 27}$



$\bold{Hence,} \\ \\ \bold{ \boxed{ \bold{27 }}\: \: small \: \: cube \: \: with \: \: an \: \: edge \: \: of \: \: 6 \: cm} \\ \bold{can \: \:be \: \: made \: \: out \: \: of \: \: a \: \: cuboid \: \: measures } \\ \bold{of \: \: 27 \: \: cm \times 18 \: \: cm\times 12 \: \: cm \: \: assuming \: \: } \\ \bold{that \: \: there \: \: is \: \: no \: \: wastage \: \: in \: \: this \: \: process.}$

Answer 2

$\underline{ \underline{ \pink{ \mathbb{ \: \: SOLUTION \: \: }}}}$

$Measures \: \: of \: \: \: the \: \: cuboid = 27 \: \: cm \times 18 \: \: cm \times 12 \: \: cm \\ \\ So, \\ \\ Volume \: \: of \: \: the \: \: cuboid =( 27 \times 18 \times 12) \: \: cm {}^{3} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 5832 \: \: cm {}^{3}$


$Again ,\\ \\ Edge \: \: of \: \: the \: cube = 6 \: \: cm \\ \\ So ,\\ \\ Volume \: \: of \: \: the \: \: cube = (6) {}^{3} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 216 \: \: cm{}^{3}$


$Thus, \\ \\ No. \: \: of \: \: such \: \: cube \: \: made \: \: from \: \: the \\ cuboid = \frac{ \: \: Volume \: \: of \: \: the \: cuboid \: \: }{Volume \: \: of \: \: the \: \: cube} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{5832 \: \: cm {}^{3} }{216 \: \: cm {}^{3} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 27$


$Therefore \\ \\ \underline{ \: \: 27 \: \: } \: \: such \: \:small \: \: cube \: \: can \: \: be \: \: made \: \: out \: \: of \: \: \\ the \: \: big \: \: cuboid \: \: assuming \: \: that \: \: no \: \: wastage \\ is \: \: made \: \: in \: \: this \: \: process.$