Question

A circle is growing, its radius increasing by 5 mm per second. Find the rate at which the area is changing at the moment when the radius is 22 mm. When the radius is 22 mm, the area is changing at approximately

Answer 1

The rate at which the area of the circle is changing at the moment the radius is 22 mm is 220π mm²/s.

Step-by-step explanation:

To find the rate at which the area of a circle is changing as the radius increases, we differentiate the area formula with respect to time. The formula for the area of a circle is A = πr^2, where r is the radius.

So, when the radius is 22 mm, we have A = π(22)^2 = 484π mm^2. Then, we differentiate the area formula with respect to t (time): dA/dt = 2πr(dr/dt).

Given that dr/dt = 5 mm/s, we can substitute this value into the equation to find the rate at which the area is changing at the moment when the radius is 22 mm: dA/dt = 2π(22)(5) = 220π mm²/s.