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? - Mathematics

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Sum

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

  Is there an error in this question or solution?
Chapter 6: Application of Derivatives - Exercise 6.1 [Page 197]

APPEARS IN

NCERT Mathematics Class 12
Chapter 6 Application of Derivatives
Exercise 6.1 | Q 4 | Page 197

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