Given as the edge of a variable cube is increasing at the rate of 3 cm per second.
Find the rate of volume of the cube increasing when the edge is 1 cm long
Suppose the edge of the given cube be x cm at any instant time.
Now according to the given question can be write as
The rate of edge of the cube increasing is, dx/dt = 3cm/sec ...(i)
Now the volume of the cube at any time t will be
V = x3cm3
By applying derivative with respect to time on both sides
From the equation (i)
When edge of the cube is 1cm long, the rate of volume increasing becomes
dV/dt = 9 x (1)2 = 9cm3/sec
Thus, the volume of the cube increasing at the rate of 9cm3/sec.
