Question

Find the volume of a cube ,one face of which has an area of 64cm^2

Answer 1

Area of one face of cube = 64cm²
=>side×side = 64
=>side = √64
=>side = 8

Each side of cube = 8cm

Volume of cube
= (side)³
= (8)³
= 512cm³

Answer 2

$\large \bold{ \underline{ \underline{ \sf \: Answer : \: \: \: }}}$

$\to$ 512 cm³

$\large \bold{ \underline{ \underline{ \sf \: Explaination : \: \: \: }}}$

$\star$ One face of the cube is called square

Therefore ,

$\large\bold{ \fbox{ \fbox{ \: \sf Area \: of \: square = { ( Side )}^{2} \: }}}$

$\to \sf {(a)}^{2} = 64 \\ \\ \to \sf</p><p>a = 8 \: cm$

So , side of the cube wiil be 8 cm

Now ,

$\large \bold{ \fbox{ \fbox{ \: \sf Volume \: of \: cube = {(a)}^{3} \: }}}$

$\to \sf Volume \: of \: cube = {(8)}^{3} \\ \\ \to \sf</p><p>Volume \: of \: cube = 512 \: {cm}^{3}$

Hence , the required value is 512 cm³