Wa1337 said:Homework Statement
A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3 ft/s. Does the area also increase at a constant rate?
Homework Equations
A = ∏r2
The Attempt at a Solution
dA/dt = 2∏r(dr/dt)
dA/dt = 2∏r(3ft/s)
What now?
The area of a circle is calculated by multiplying pi (π) by the square of the radius (r), or A = πr^2.
The area of a circle is directly proportional to the square of the radius. This means that as the radius increases, the area also increases, and as the radius decreases, the area decreases.
Related rates refer to the relationship between two changing quantities. In the context of finding the rate of change of the area of a circle, the radius and the area are related to each other and are both changing over time.
To find the rate of change of the area of a circle with respect to time, you can use the related rates formula: dA/dt = 2πr(dr/dt). This formula takes into account the changing radius and the constant value of pi (π).
No, the rate of change of the area of a circle can never be negative. The area of a circle is always a positive value, and as the radius increases or decreases, the area will also increase or decrease, respectively.