Respuesta :
Answer:
The area is changing by the rate of 44.62 meters per sec.
Step-by-step explanation:
Let x be the side of the square and r be the radius of the circle,
Then, the area outside the circle but inside the square is,
V = Area of square - area of circle,
∵ Area of a square = side² and area of a circle = [tex]\pi[/tex] (radius)²,
Thus,
[tex]V=x^2-\pi(r)^2[/tex]
Differentiating with respect to t ( time )
[tex]\frac{dV}{dt}=2x\frac{dx}{dt} -2\pi r\frac{dr}{dt}[/tex]
We have,
x = 20 meters, r = 3 meters, [tex]\frac{dx}{dt}=3\text{ m per sec}[/tex] [tex]\frac{dr}{dt}=4\text{ meters per sec}[/tex]
[tex]\implies \frac{dV}{dt}=2(20)(3)-2\pi(3)(4)[/tex]
[tex]=120-24\pi[/tex]
[tex]=44.6017763138[/tex]
[tex]\approx 44.62\text{ meter per sec}[/tex]
