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a box has a width of 15 inches and a length of 16 inches. the volume of the box is increasing at a rate of 569 cubic inches per second, with the width and length being held constant. what is the rate of change, in inches per second, of the height when the height is 6 inches?



Answer :

varshamittal029

The rate of change in height when height is 6 inches is 2.37 inches per second approximately.

We know that the volume of cube with length L, width W and height H is given by,

V = L*B*H

So given that the length is 15 inches

the width is 16 inches

Let the height be h inches.

So now the volume is given by,

V = 15*16*h

Differentiating the volume with respect to time 't' we get,

dV/dt = 15*16 dh/dt

Now given that the rate of change in volume per second is 569 cubic inches.

So, dV/dt = 569

So, 15*16 dh/dt = 569

dh/dt = 569/(15*16) = 569/240 = 2.37 (approx)

So the rate of change in height is 2.37 inches approximately.

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