Do 4x and 15 + x have the same value when x is 5? How do you know?
2 answers:
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Answer:
Step-by-step explanation:
Here's the formula for the volume of a right circular cylinder:
Here's what we are given and what we need to find:
Given that d = 10 cm, h = 20 cm, dd/dt = 1 cm/sec
Need to find dh/dt when V is constant
Since our formula has a radius in it and not a diameter but the info given is a diameter, we can use the substitution that
so
Now we can rewrite the formula in terms of diameter:
which simplifies down to
Now we will take the derivative of this equation with respect to time using the product rule. That derivative is
Now we can fill in our values. Keep in mind that if the volume is constant, there is no change in the volume, so dV/dt = 0.
and
Multiply both sides by pi/4 to get
and solve for dh/dt:
Interpreted within the context of our problem, this means that the volume will be constant at those given values of diameter and height when the liquid in the cylinder is dropping at a rate of 4 cm/sec.