Related Rates: Finding the Area Change of a Snowball with Changing Radius

[hunter55]

Homework Statement

a snowball is rolling donw a hill, its radius is changing at a rate of 2 cm/min. what is the rate of change of the area, when the radius is 8 cm?

Homework Equations

da/dt= 2pir2dr/dt
dat/dt=2pi(8)(2)
32pi ?
is that right

The Attempt at a Solution

32pi

 

[Dick]

What formula are you using for A? If you are thinking of the snowball as a disk and A=pi*r^2, then yes, dA/dt=pi*2*r*dr/dt. You might want to put units on your answer.

 

[HallsofIvy]

As Dick suggested, you are using the wrong formula (because a snowball is NOT a disk). The "area'' referred to here is the SURFACE area of a sphere.
Surface area of a sphere is $4\pi r^2$.

(And, of course, be sure to put units on your answer.)