# Question of the Week 11: Area of a Circle

I created the above question especially for my delightful Year 11 set. We were going through a practise GCSE exam paper, and we came to a question about calculating the area of a circle. Under normal circumstances, this would cause them no issues – they would reach for their trusty calculators and everyone would be happy. However, this particular question appeared on the non-calculator paper, and contained those 7 dreaded words: “give your answer in terms of pi”.

This was met with a combination of sighs, shrugs, a few tears, and crucially very little logical mathematics that would have gained them any marks.

It got me thinking that giving answers in terms of pi should make circle questions easier, as it avoids the potentially distracting never-ending stream of decimal places, but it can actually complicate things in the minds of students.

Having spent the remainder of the lesson ensuring students were happy with the idea that the pi symbol is just a number, I followed it up with the question above at the start of the next lesson.

Here is my logic behind each of the answers:

Answer A) here, students may simply square the diameter instead of finding the radius, hence revealing that they have a misconception with the area of a circle formula itself

Answer B) may imply that students are muddling up the formula for area of a circle with that for working out the circumference