Standard +0.3 This is a standard related rates calculus problem requiring the chain rule to connect dV/dt to dA/dt via dr/dt. While it involves multiple steps (find dr/dt from volume rate, then use it to find dA/dt), the setup is straightforward with all formulas provided, making it slightly easier than average for A-level Further Maths.
A spherical balloon is inflated so that its volume increases at a rate of \(10\text{ cm}^3\) per second.
Find the rate of increase of the balloon's surface area when its diameter is 8 cm.
[For a sphere of radius \(r\), surface area \(= 4\pi r^2\) and volume \(= \frac{4}{3}\pi r^3\)]. [5]
A spherical balloon is inflated so that its volume increases at a rate of $10\text{ cm}^3$ per second.
Find the rate of increase of the balloon's surface area when its diameter is 8 cm.
[For a sphere of radius $r$, surface area $= 4\pi r^2$ and volume $= \frac{4}{3}\pi r^3$]. [5]
\hfill \mbox{\textit{SPS SPS FM Pure 2023 Q6 [5]}}