Question

Find the volume of a cube, one face of which has an area of 64 m².

Answer 1

Area of a face of cube is given by:
$A=s^2$, where s = Side of the cube

Further, volume of a cube is given by:
$V=s^3$, where s = Side of the cube

It is given that the area of one face of the cube is 64 m². Therefore we have:

$s^2=64\Rightarrow s=\sqrt{64}=8\text{m}$

Now, volume is given by:

$V=s^3=8^3\Rightarrow V=8\times 8\times 8=512{\text{m}}^3$

Thus, the volume of the cube is 512 m³.