Answer
The equation given in the textbook says that the change in length $\Delta L$ of a material is given by $\Delta L = \alpha \Delta T$. This is incorrect. The correct equation is $\Delta L = L \cdot \alpha \cdot \Delta T$.
Here, the length L is the length of the pipe circling the Earth, given as 40,000,000 m.
$$\Delta L = L \cdot \alpha \cdot \Delta T = (40,000,000 m)(\frac{11 \times 10^{-6}}{^{\circ}C})(1^{\circ} C) = 440 m$$
The snugly fitting steel pipe lengthens by 440 m when heated. The length L = $2 \pi r$, so the change in L results in a change in R of $\frac{440 m}{2 \pi} = 70 m$.
