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


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