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Question 4:
An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?
Let x be the length of a side and V be the volume of the cube. Then,
V = x3.
∴
(By chain rule)
It is given that,
∴
Thus, when x = 10 cm,
Hence, the volume of the cube is increasing at the rate of 900 cm3/s when the edge is 10 cm long.
