Asked Oct 1, 2019

The length ℓ, width w, and height h of a box change with time. At a certain instant, the dimensions are ℓ = 6 m and w = h = 3 m, and ℓ and w are increasing at a rate of 1 m/s while h is decreasing at a rate of 9 m/s. At that instant find the rates at which the following quantities are changing.

a) The volume.

b) The surface area.

c) The length of the diagonal. (Round answer to two decimal places)


Expert Answer

Step 1

It is given that, the length(l), width(w) and height(h) of a box change with time(t).

And at a certain instant, length(l)=6m, width(w)= 3m and height(h)=3m.



Image Transcriptionclose

dl Ims dt dwms -1 dt dh -9ms dt

Step 2

To find the rate at which the following quantities are changing at time(t).

  • Volume
  • Surface Area
  • Length of the diagonal
Step 3
  • The rate of change of the volum...

Image Transcriptionclose

dV d (.w.h) dt dt dV d =1.-(w.h)w.h-(I) dt d dt dt dw h. dt dV dh W. dt dl w.h. dt dt dl dwwh- dV dh lw +lh dt dt dt dt = lwh'+lw'h+ l'wh... dt .(1)


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