Explanation:
my previous answer assumed we need a kind of average change rate.
but it seems you need the immediate change rate ?
or what ? the question does not specify.
I would appreciate if you would leave a comment, when you find that my answer is seemingly not matching some expected answers.
so, let's try now the immediate change rate (as I have no information to go - I have also no information about what you are currently learning in your class, and if you do already derivatives or not, so, this might be now above your learning level ...) :
again, the area between the inner circle and the outer square is
A = As - Ac = s² - pi×r²
where s is the square's side length, and r is the radius of the circle.
the immediate change rate of that area is the sum of first derivatives of A based on both used variables multiplied by their individual change rates :
dA/dt = dAs/ds × ds/dt - dAc/dr × dr/dt
and this is then calculated for the given data point (s = 16, r = 3) and the individual change rates of the variables (ds/dt = 2 meters/minute, dr/dt = 1 meter/minute).
so, we have
dA/dt = 2s × 2 - 2×pi×r × 1
as (s²)' = 2s, (pi×r²)' = 2×pi×r
dA(16, 3)/dt = 2×16×2 - 2×pi×3×1 = 64 - 6pi =
= 45.15044408... meters²/minute ≈
≈ 45.15 meters²/minute
so, you see, for a curved function (not a line) there has to be a difference between the average change rate between 2 points and the immediate change rate directly at a point.
I hope this works now for you.
and here now the original answer for an average change rate :
right now the radius is 3 m, and the square side lengths are 16 m.
1 minute ago the radius was 2 m, and the square side lengths were 14 m.
the area between the circle and the square is always the area of the square minus the area of the circle.
these areas are right now
circle : pi×3² = 9pi m²
square : 16² = 256 m²
area between = 256 - 9pi = 227.7256661... m²
these areas were one minute ago
circle : pi×2² = 4pi m²
square : 14² = 196 m²
area between = 196 - 4pi = 183.4336294... m²
the change rate of the area between the circle and the square is
227.7256661... - 183.4336294... = 44.29203673... m² per minute