The area A of a circle is increasing at a constant rate of 1.5 cm² s⁻¹ - Edexcel - A-Level Maths Pure - Question 8 - 2010 - Paper 7

Given that ( \frac{dA}{dt} = 1.5 ) cm² s⁻¹ and when ( A = 2 ) cm², we can find the radius:

$2 = \pi r^2 \Rightarrow r = \sqrt{\frac{2}{\pi}} \approx 0.797884$

Now substitute the values into the differentiated equation:

$1.5 = 2\pi r \frac{dr}{dt}$

Solving for ( \frac{dr}{dt} ):

$\frac{dr}{dt} = \frac{1.5}{2\pi r}$

Substituting ( r \approx 0.797884 ):

$\frac{dr}{dt} \approx \frac{1.5}{2\pi (0.797884)} \approx 0.299$

Thus, the rate at which the radius of the circle is increasing when the area is 2 cm² is approximately 0.299 cm s⁻¹.