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 1 cm long?
Given: the edge of a variable cube is increasing at the rate of 3 cm per second.
To find rate of volume of the cube increasing when the edge is 1 cm long
Let the edge of the given cube be x cm at any instant time.
Then according to the given criteria,
Rate of edge of the cube increasing is,
Then the volume of the cube at any time t will be
V = x3 cm3.
Applying derivative with respect to time on both sides we get,
[from equation(i)]
When the edge of the cube is 1cm long the rate of volume increasing becomes
Hence the volume of the cube increasing at the rate of 9cm3/sec when the edge of the cube is 1 cm long