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Answer:
-3.47 inches per minute
Step-by-step explanation:
Let the height be 'h' for any time 't'.
Given:
Length of the prism (L) = 10 in
Width of the prism (w) = 16 in
The rate of change of volume of prism is, (The negative sign implies the volume decreases with time.)
Now, rate of change of height of prism =
Length and width remains constant.
Now, we know that, volume of a rectangular prism is given as:
Volume = Length × width × Height
Now, differentiating both sides with respect to time 't', we get:
Plug in the given values and solve for . This gives,
The negative sign implies the height decreases with time.
Therefore, the the rate of change, in inches per minute, of the height when the height is 3 inches is -3.47 inches per minute.