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: \[s^2 = 64 \Rightarrow s = \sqrt{64} = 8 m\]

Now, volume is given by:

\[V = s^3 = 8^3 \Rightarrow V = 8 \times 8 \times 8 = 512 m^3\]

Thus, the volume of the cube is 512 m³.