Question

2. The area A of a circle is increasing at a constant rate of 2.5cm s . If the area of the circle is given

by A = πr2, what is the rate of change of the radius when the radius is 15cm?

Answer 1

235.65 cm^2s-1

Explanation:

We have that;

Rate of change of area (dA/dt) = (dA/dr) (dr/dt) By chain rule

Note that dr/dt = rate of change of radius

But

A = πr^2

dA/dr = 2πr

dr/dt = 2.5cm s-1 (given)

So;

dA/dt = 2πr * 2.5cm s-1

r = 15cm (given)

dA/dt = 2 * 3.142 * 15cm * 2.5cm s-1

dA/dt = 235.65 cm^2s-1