Answers and workings in the attachment below.
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Answer:
So the radius is increasing at .
This is approximately 0.00497 cm/min that the radius is increasing.
Step-by-step explanation:
The volume and radius are both things that are changing with respect to time.
So their derivatives will definitely not be 0.
Let's differentiate:
I had to use constant multiple rule and chain rule.
We are given and
.
We want to find .
Let's plug in first:
Multiply both sides by 3:
Divide both sides by :
So the radius is increasing at .
This is approximately 0.00497 cm/min that the radius is increasing.