Question

The perimeter of a square is increasing at a rate of 555 meters per hour. At a certain instant, the perimeter is 303030 meters. What is the rate of change of the area of the square at that instant (in square meters per hour)

Answer 1

Answer: $21,022,706.3\ m^2/hr$

Step-by-step explanation:

Given

The rate of change of perimeter of a square is increasing at a rate of $555\ m^3/hr$

At a certain instant, the perimeter is $303030\ m$

At this instant side of square is

$\Rightarrow a=\dfrac{303030}{4}\\\\\Rightarrow a=75,757.5\ m$

Rate of change of perimeter is

$\Rightarrow \dfrac{dp}{dt}=4\dfrac{da}{dt}\\\\\Rightarrow 555=4\dfrac{da}{dt}\\\\\Rightarrow \dfrac{da}{dt}=138.75\ m/hr$

At this instant, rate of change of the area of the square is

$\Rightarrow A=a^2\\\Rightarrow \dfrac{dA}{dt}=2a\dfrac{da}{dt}\\\\\Rightarrow \dfrac{dA}{dt}=2\times 75757.5\times 138.75\\\\\Rightarrow \dfrac{dA}{dt}=21,022,706.3\ m^2/hr$