Question

Find the volume of a cube whose surface area is 384 m².

 

Answer 1

Surface area of a cube is given by:

\[SA = 6 s^2\], 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 surface area of the cube is 384 m². Therefore, we have:

\[6 s^2 = 384 \Rightarrow s = \sqrt{\frac{384}{6}} = \sqrt{64} = 8 m\]

Now, volume is given by:

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

Thus, the required volume is 512 m³.