Question

If the lateral surface area of a cube if its volume is 512 cm cube​

Answer 1

${\sf \: {1024\sqrt{2} \: {cm}^{3}}}$

GiVen:-

• Volume of the cube =512cm

AnSwer:-

$\\ \bigstar\sf \: Lateral \: Surface \: Area \: of \: a \: Cube : - \\ \\ \implies \sf \: 4 {a}^{2} \\ \\\implies \sf \: 512$

$\bigstar{ \sf{ \underline{According \: to \: the \: question, }}}$

$\implies \sf \: {a}^{2} = 512/4 \\ \\ \implies \sf \:a = \sqrt{128} \\ \\ \implies \sf \:a = 8 \sqrt{2} cm$

$\bigstar \sf \: Volume : - \\ \\ \sf \implies {a}^{3} \\ \\ \sf \implies \: {(8 \sqrt{2} )}^{3}$

${\implies{\sf \: {1024\sqrt{2} \: {cm}^{3}}}}$

Answer 2

Let each side of the cube be a cm

$Volume \:of \: cube = 512^3$

$a^3 = 512$

$a = 3√512$

$a = 8cm$

$Total \:surface\: area of \:cube = 6a^2$

$6 × 8^2 => 6 × 84 = 384 cm^2$