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

75/4

Explanation:

Answer 2

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

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=(303030)/(4)\\\\\Rightarrow a=75,757.5\ m`

Rate of change of perimeter is

`\Rightarrow (dp)/(dt)=4(da)/(dt)\\\\\Rightarrow 555=4(da)/(dt)\\\\\Rightarrow (da)/(dt)=138.75\ m/hr`

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

`\Rightarrow A=a^2\\\Rightarrow (dA)/(dt)=2a(da)/(dt)\\\\\Rightarrow (dA)/(dt)=2* 75757.5* 138.75\\\\\Rightarrow (dA)/(dt)=21,022,706.3\ m^2/hr`