If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, how do you find the rate at which the diameter decreases when the diameter is 12 cm?
1 Answer
Dec 10, 2016
diameter is decreasing at rate of
Explanation:
Assuming the snowball is a perfect sphere, then if
# A = 4pir^2 = 4pi(D/2)^2 = piD^2 #
Differentiating wrt
# (dA)/(dD) = 2piD #
We are told that
By the chain rule we have:
# (dA)/(dD) = (dA)/(dt)*(dt)/(dD) = ((dA)/(dt)) / ((dD)/dt)#
# :. 2piD = -3/ ((dD)/dt) #
# :. (dD)/dt = -3/ (2piD) #
When
The sign confirms that