Calculus question

Question

Each side of a square is increasing at a rate of 5 cm/s. At what rate is the area of the square increasing when the area of the square is 81cm^2.

Answer 1

Step 1) Write the area function in terms of the variable given in the problem.

Let "s" be the side length of the square. Then Area (A) can be calculated from:

A = s²

Step 2) Take the derivative with respect to time:

Notice that you must use the chain rule to do so.

Step 3) Plug in the values and solve

First, calculate "s" from the fact given that the area is 81 cm² at the time in question. "s" must be 9. So s= 9, and ds/dt = 5 cm/s:

dA/dt = 2(9)(5) = 90 cm²/s