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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 if 10 cm long?
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 if 10 cm long?
Applications of Derivatives | CBSE | Class 12 | Exercise 6.1 | Maths | NCERT
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 if 10 cm long?

Let  cm be the edge of variable cube at time 

Rate of increase of edge = 3 cm/sec

 is positive and = 3 cm/sec

Let  be the volume of the cube.

 

Rate of change of volume of cube =  = 

= 

=  cm3/sec

Putting  = 10 cm (given),

 =  cm3/sec

Since  is positive, therefore volume of cube is increasing at the rate of 900 cm3/sec.

i

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