Question

A) Find the average rate of change of the area of a circle with respect to its radius r as r changes from (i) 5 to 6 \rightarrow Average rate of change = (ii) 5 to 5.4 \rightarrow Average rate of change = (iii) 5 to 5.1 \rightarrow Average rate of change = (B) Find the instantaneous rate of change when r = 5 . Instantaneous rate of change =

Answer 1

from five to six
\[\pi \times 6^2-\pi \times 5^2=36\pi -25\pi = 11\pi\]

Answer 2

the rest are similar

Answer 3

what about the last part on how to find instantaneous rate of change when r = 5

Answer 4

Instantaneous
means you need to find the derivative of the area of a circle w.r.t r (since it is the r that is changing and you are to find it at r=5)

Answer 5

A=pi*r^2