Answer:
The diameter decreases at a rate of 0.053 cm/min.
Step-by-step explanation:
Surface area of an snowball
The surface area of an snowball has the following equation:
In which d is the diameter.
Implicit differentiation:
To solve this question, we differentiate the equation for the surface area implictly, in function of t. So
Surface area decreases at a rate of 3 cm2/min
This means that
Tind the rate (in cm/min) at which the diameter decreases when the diameter is 9 cm.
This is when
. So
The diameter decreases at a rate of 0.053 cm/min.