Question

If a snowball melts so that its surface area decreases at a rate of 10 cm2/min, find the rate at which the diameter decreases when the diameter is 12 cm.

Answer 1

The Surface Area of a sphere is,\[\large A=4\pi r^2\]

And they gave us the rate at which the Surface Area is decreasing,\[\large A'=-10\]

We want to write our Surface Area formula in terms of Diameter.
It is currently written in terms of the Radius.

How can we change that? :)

Answer 2

r = d/2
putting it into the equation gives
\[A = 4\pi d ^{2} \div 4\]
\[A = \pi d ^{2} \]
Take derivative in both side
\[A \prime = 2 \pi d d \prime\]
d' = -10/ 2 pi*12