Question

The radius of the circle is decreasing at a rate of 1 meter per day and the sides of the square are decreasing at a rate of 4 meters per day.

Answer 1

Step 1:

In this question, we have the following:

Step 2:

`\begin{gathered} (dr)/(\differentialDt t)\text{ = - 1m/day } \\ (dl)/(\differentialDt t)=\text{ -4 m / day} \end{gathered}`
`\begin{gathered} \text{ A = l}^2-\pir^2 \\ (dA)/(\differentialDt t)\text{ =2l}(dl)/(\differentialDt t)\text{ -2}\pi r(dr)/(\differentialDt t) \\ =\text{ 2l ( - 4 ) - 2}\pi r(-1) \\ =\text{ -8l +2}\pi r \\ =\text{ -8(15) + 2}\pi(4) \\ =\text{ -120 + 8}\pi \end{gathered}`
`\begin{gathered} \text{Assume }\pi\text{ = 3.142} \\ =\text{ -120 + 8 ( 3. 142)} \\ =\text{ -120 + 25.136} \\ =\text{ -94.864 square meters per day} \end{gathered}`