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Question
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?
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Solution
Let the length of the cube = x cm
= Volume of the cube, V = x3
Given, `dx/dt = 3` cm/s
= Rate of change of V with respect to t, `(dV)/dt = 3x^2 dx/dt`
`= (dV)/dt = 3x^2 (3)`
`= (dV)/dt = 9x^2`
`= 9 xx (10)^2 `
= 900 cm3/sec
=> Rate of increase of volume of cube is 900 cm3/sec
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