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

We know that the rate of change of area is given as:

$\frac{dA}{dt} = 1.5 \, \text{cm}^2/s$

We need to find the radius r when the area A is 2 cm²:

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

Now we can substitute the values into our earlier derived equation:

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

From this equation, we can solve for (\frac{dr}{dt}):

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

Now performing the calculation gives:

$\frac{dr}{dt} \approx \frac{1.5}{2\pi(0.797884)} \approx 0.299 \text{ cm/s}$

Thus, the rate at which the radius is increasing when the area is 2 cm² is approximately 0.299 cm/s.