the area of a circle increasing at the rate of 3cm/sec.find the rate of change of the circumference when the radius is 2cm
help plz
1.5
A = π r^2
dA/dt = 2π r dr/dt
given: dA/dt = 3 , find dr/dt when r = 2
3 = 2π (2) dr/dt
dr/dt = 3/(4π) cm/s
34
To find the rate of change of the circumference when the radius is 2cm, we need to use the relationship between the circumference and the radius of a circle.
The formula to calculate the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
Given that the area of the circle is increasing at a rate of 3 cm/sec, we can determine the rate of change of the circumference.
To find the rate of change of the circumference, we differentiate the formula for the circumference with respect to time (t):
dC/dt = d/dt(2πr)
Next, substitute the given radius value of 2cm into the equation:
dC/dt = d/dt(2π(2))
Simplifying further:
dC/dt = 4π
Therefore, the rate of change of the circumference when the radius is 2cm is 4π cm/sec.
So, the rate of change of the circumference is 4π cm/sec.