| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable acceleration (1D) |
| Type | Related rates with spheres, circles, and cubes |
| Difficulty | Standard +0.3 This is a standard related rates problem requiring the chain rule and the sphere volume formula. While it involves calculus, it's a straightforward single-step application with clear setup, making it slightly easier than average for C3 level. |
| Spec | 1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
\begin{enumerate}
\item A balloon is filled with air at a constant rate of $80 \mathrm {~cm} ^ { 3 }$ per second.
\end{enumerate}
Assuming that the balloon is spherical as it is filled, find to 3 significant figures the rate at which its radius is increasing at the instant when its radius is 6 cm .\\
\hfill \mbox{\textit{OCR C3 Q1 [5]}}