I was with a 2nd year high school class, preparing for our (US) state's standardized test. I asked the class how they would solve this, and they flipped through the sheets to find
(To be clear, there is a 'formula' page that's given with the exam.) As they fumbled with their calculators, I asked them what the radius was. 3.5. and I wrote the numbers on the board.
I attempted to show them how 3.5 squared is close enough to 12. Divide by 3 to get 4, and we are left with 36pi. Since 36x3 is 108, the only answer that can make sense is 115.
In my lecture, I offered 3 benefits of this process. (1) The speedy approach can save precious time on this type of question so more time remains for those requiring more thought and time. (2) If you still use the calculator, this is a good double check to be sure the answer makes sense, that you didn't hit the wrong key. (3) If you forget your calculator, the proctor won't always have an extra, and the whole exam can be done by hand.
Out of the 12 questions we did as a group, a full half lent themselves to this method, as number were easy to round, and the answers were different enough so cumulative rounding errors didn't inch results too far away from the true answer. After my second attempt, on the next appropriate question, to explain this approach, I realized it wasn't helpful to this class and I stopped.
I recall that as a student, estimating was a skill that we were taught as part of the regular math class. Is this no longer considered to be valuable?