Question

Surface area of a cube is
$216 {}^{2} cm$
what is it's volume?​

Answer 1

Step-by-step explanation:

$Let \: the \: to edge \: of \: the \: cube \: be \: a.$

$Surface \: area \: of \: cube = 6×edge²$

$\implies 216cm² = 6a²$

$\implies a² = \frac{216}{6}$

$\implies a² = 36$

$\implies a = 6$

$So, \: the \: edge \: of \: the \: cube \: is \: 6cm.$

$Now, \: the \: vol. \: of \: cube = edge³$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (6cm)³$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 216cm³$

$Hence, \: the \: vol. \: of \: the \: cube \: is \: 216 \: cm³.$