Mathematics

This problem chains together two relationships: volume depends on temperature, and temperature depends on time. You need the chain rule to find how volume changes with time directly. Rather than substituting $T$ into $V$ first, recognize that $\frac{dV}{dt} = \frac{dV}{dT} \cdot \frac{dT}{dt}$—find each piece separately, then multiply them together at the specific moment $t = 10\,\text{s}$.

This problem chains together two relationships: volume depends on temperature, and temperature depends on time. You need the chain rule to find how volume changes with time directly. Rather than substituting $T$ into $V$ first, recognize that $\frac{dV}{dt} = \frac{dV}{dT} \cdot \frac{dT}{dt}$—find each piece separately, then multiply them together at the specific moment $t = 10\,\text{s}$.