A paint tin is leaking, a circular

puddle is formed and the radius of the

circle increases at a constant rate.

a) If the circumference of the circle

is increasing at a rate of 12cm/s, find

the rate at which the radius is increasing.

The rate at which the radius is increasing

dr/dt = 1.91 cm/s

Step-by-step explanation:

The circumference C of a circle can be written as;

C = 2πr ... 1

Where;

r = radius

The rate at which the circumference of the circle

is increasing can be written as dC/dt;

Differentiating equation 1, we have;

dC/dt = 2π dr/dt

Making dr/dt the subject of formula;

dr/dt = (dC/dt) / 2π

Given;

dC/dt = 12cm/s

Substituting the value of dC/dt;

dr/dt = 12/2π

dr/dt = 1.909859317102 = 1.91 cm/s

The rate at which the radius is increasing dr/dt is 1.91 cm/s