Question #d1bd0
1 Answer
Feb 7, 2018
The rate is
Explanation:
Let us set up the following variables:
# { (t,"time", min), (r, "radius at time "t, cm), (A, "Area of the circle at time "t, cm^2) :} #
The area of the circle is:
# A=pir^2 #
Differentiating wrt
# (dA)/(dr) = 2pir #
Using the chain rule we can write:
# (dA)/(dt) = (dA)/(dr) \ (dr)/(dt)#
We are given that the radius
# (dA)/(dt) = 4 \ (dA)/(dr) = 8pir#
So when
# (dA)/(dt) = 8pi xx 12 #
# \ \ \ \ \ \ = 96pi#
# \ \ \ \ \ \ ~~ 301.59 \ (2dp) \ cm^2 \ mi n^(-1)#