Open Middle®
Directions: If possible, find the radius of a circle where the area of the circle and the circumference of the circle are equal. Is there more than one possible answer?
Hint
How do we find the area of any circle?
How do we find the circumference of any circle?
Is there a way for these to have the same value?
How do we find the circumference of any circle?
Is there a way for these to have the same value?
Answer
The radius would have to be 2 units.
Source: Karen Bloom
I’m thinking about the potential misconceptions this might cause by using the word “equal”. I know what’s meant but in thinking about this, the area and circumference are never equal because the circumference will be 4pi units and the area will be 4pi square units.
Not sure how to modify this one.
Does this present an excellent discussion opportunity with the students?
Ask “Does anyone see a problem with this equivalency” and allow them to come to this conclusion, even if with some further questioning/hints/
Hi Robert,
What if you re-phrased slightly to “make the area and perimeter numerically equal” ?
“Numerically equal” is exactly what I was thinking as well.