Volume of a Cube The volume V of a cube with sides of length x in. is changing with respect to time. At a certain instant of time, the sides of the cube are 7 in. long and increasing at the rate of 0.2 in./s. How fast is the volume of the cube changing (in cu in/s) at that instant of time?

Therefore the volume of cube is change at the 29.4 cube in./s at that instant time.

Explanation:

Formula

Cube :

The volume of a cube is =

The side of length is x in.

Then volume of the cube is (V) =

∴ V =

Differentiate with respect to t

....(1)

Given that the side of the cube is increasing at the rate of 0.2 in/s.

i.e  in/s.

And the sides of the cube are 7 in i.e x= 7 in

Putting  and  x= 7 in equation (1)

 cube in./s

       =29.4 cube in./s

Therefore the volume of cube is change at the 29.4 cube in./s at that instant time.

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