First, we {{CMD_26}}introduce the variables{{CMD_27}} {{MATH_28}}, {{MATH_29}}, and {{MATH_30}}, denoting the perimeter, the radius, and the area of the circle, in that order. We {{CMD_31}}identify{{CMD_32}} the given rate, {{MATH_33}} m/s, and the unknown rate, {{MATH_34}}, at the moment when {{MATH_35}}. Next, we {{CMD_36}}draw a picture{{CMD_37}}. {{CMD_38}} {{ENV_39}} {{CMD_40}} Now we have to {{CMD_41}}find equations{{CMD_42}} that relate the variables {{MATH_43}}, {{MATH_44}}, and {{MATH_45}}. Naturally, we think of formulas for perimeter and area of a circle {{MATH_46}} We know that the perimeter of the circle is expanding. This implies that both the radius and the area of the circle are changing in time, too. So, we note that {{MATH_47}}, {{MATH_48}}, and {{MATH_49}} are functions of time {{MATH_50}} We {{CMD_51}}differentiate{{CMD_52}} both sides of each equation with respect to time, {{MATH_53}}. Using implicit differentiation, we get that {{MATH_54}} These two equations hold on some time interval. In particular, they are both true at an instant when {{MATH_55}}.