Question

Find the side of cube if it's total surface area is 486 cm²

Answer 1

$\mathtt{ \huge{ \purple{ \underline{\fbox{ \orange{ \: Solution \: \: : }}}}} }$

Given ,

The total surface area of cube = 486 cm²

We know that , the TSA of cube is given by

$\large \sf \fbox{Total \: surface \: area = 6 \times {(side)}^{2} }$

Substitute the values , we obtain

$\sf \hookrightarrow 486 = 6 \times {(side)}^{2} \\ \\ \sf \hookrightarrow {(side)}^{2} = \frac{486}{6} \\ \\ \sf \hookrightarrow side = \sqrt{81} \\ \\ \sf \hookrightarrow side = 9 \: \: cm$

Hence , the side of cube is 9 cm

Answer 2

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