Question

Find the volume of a solid cube whose total surface area is 486 square meter
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Answer 1

Step-by-step explanation:

surface area of cube= 486

6a^2 = 486

a^2= 486/6

a^2 = 81

a = √81

a= 9

volume of cube = a^3

= 9×9×9

=729 m^3

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Answer 2

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