Question

Find the volume of a cubical box whose surface area is 486cm2

Answer 1

6a2=486
a2=81
a=9
hence volume is a3=729 cm3

Answer 2

$\textbf{\huge\underline{\underline\red{Solution} : - }} \\ \\\textbf{\underline{\red{given} : - }} \: \: \bold{surface \: area\: of \: cube \: is \:} \\ \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 486 \: {cm}^{2} } \\ \\ \textbf{\underline{\red{to \: find} : - } } \: \bold{volume \: of \: cube.} \\ \\ \textbf{\underline{\red{formula} : - }} \: \\ \\ \bold \purple{surface \: area \: of \: cube \: = 6 {a}^{2} } \\ \\ \bold \purple{ \: volume \: of \: cube \: = {a}^{3} } \\ \\ \bold\red{where \: \: \purple{a} \: \: is \: edge \:of \: cube. } \\ \\ \bold{\underline \red{now}} \\ \\ = > \bold \purple{surface \: area \: of \: cube \: = 6 {a}^{2} } \\ \\ = > \bold \purple{486= 6 {a}^{2} } \\ i.e\\ = > \bold \purple{6 {a}^{2} = 486} \\ \\ = > \bold \purple{ {a}^{2} = \frac{486}{6} } \\ \\ = > \bold \purple{{a}^{2} = 81}\\ \\ = > \bold \purple{{a} = \sqrt{81} }\\ \\ = > \bold \purple{{a} = \: 9 \:cm} \\ \\ \bold{\underline \red{now}} \\ \\ = > \bold \purple{ \: volume \: of \: cube \: = {a}^{3} } \\ \\ = > \bold \purple{ \: volume \: of \: cube \: = {9}^{3} } \\ \\ = > \bold \purple{ \: volume \: of \: cube \: = 9 \times 9 \times 9 } \\ \\ = > \bold \purple{ \: volume \: of \: cube \: = 81 \times 9} \\ \\ = > \bold \purple{ \: vomeu \: of \: cube \: = 729 \: {cm}^{3} } \\ \\ \fbox{\bold \red{ hence \: volume \: of \: cube\: box \: is \: 729 \: {cm}^{3} }} \\ \\ \underline{ \bold\blue{ \: i \: hope \: it \: helps \: you.}}$