The volume of a cube is increasing at a constant rate. Prove that the increase in surface area varies inversely as the length of the edge of the cube.

Explanation

`therefore` Volume of cube `({V})={x}^{3}`


On differentiating both side w.r.t..t, we get



`frac{d V}{d t}=3 x^{2} frac{d x}{d t}=k `


`Rightarrow frac{d x}{d t}=frac{k}{3 x^{2}}`



Also, surface area of cube, `S=6 x^{2}`


On differentiating w.r.t.t, we get


...