To solve this, let's define the following:

• Let $T_f$ represent the final temperature the lamb needs to reach.
• The internal temperature of the lamb before it went into the oven was $T_f - 41$ (41 degrees below the final temperature).
• The internal temperature of the lamb when it was removed from the oven was $T_f - 6$ (6 degrees below the final temperature).

The change in internal temperature, $\Delta T$, can be calculated as the difference between the temperature when removed from the oven and the initial temperature:

$\Delta T = (T_f - 6) - (T_f - 41).$

Simplify the expression:

$\Delta T = T_f - 6 - T_f + 41 = 41 - 6 = 35.$

Thus, the internal temperature changed by $35^\circ \text{C}$.

Matching the Situation to an Equation

The correct equation matching the situation is:

$(T_f - 6) - (T_f - 41) = 35.$

This equation captures the change in temperature explicitly.

Let me know if you'd like further clarification or details! Here are five related questions to expand your understanding:

1. How would this situation change if the initial temperature was expressed in Fahrenheit instead of Celsius?
2. How is the concept of equilibrium used in this situation?
3. Can we create a graph representing the temperature change over time for this process?
4. How would the calculation differ if Josiah had taken the lamb out at $10^\circ \text{C}$ below the final temperature?
5. How does the temperature difference affect the cooking time?

Tip: Always confirm your initial and final values when solving real-world problems involving changes in temperature or other quantities!