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Question -

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?



Answer -

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 question we can write as

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