An edge of a variable cube is increasing at the rate of 3 cm per second. How fast is the volume of the cube increasing when the edge is 10 cm long?

Explanation

Let x be the edge of cube and V be the volume.
Given ` (dx)/(dt) = 3 cm//sec`
Now ,` V=x^(3) rArr (dV)/(dt) = 3x^(2)(dx)/(dt)`
at x = 10 cm
` (dV)/(dt) = 3 xx 10^(2) xx 3 = 900 cm^(3)//sec`