Subject: Area of a circle
Q & Q:
Please don't think this a stupid question but at 44 years old, I haven't figured out the formula steps to fiding the area of a circle. I know the formula is-- pi r squared--. For a circle 4 inches in diameter, do I multiply pi (3.1416) by the radius (2") then square the answer to that ie: 3.1416 X 2 squared or do I square the radius (2 X 2") then multiply by pi (3.1416) ?? This has kept me up nights trying to figure it out because I need it for some of my work. Please help me !!
This is not a stupid question at all. The confusion comes from the fact that common English is not as precise as mathematics. The English phrase --pi r squared-- does not indicate which of your two interpretations is correct. In mathematics we either use parentheses or other conventions to indicate which operation to perform first, the multiplication of pi times r (and then square) or the squaring of r (and then multiply by pi).
The correct interpretation is to first square the radius and then multiply by pi. Thus for your circle with diameter 4 inches the area is 3.1416 (2x2) = 12.5664 square inches.
Mathematically I would write this as pi r2 since the convention is that you perform any exponentiations (the square) before multiplication. In English a more explicit phase than --pi r squared-- would be --pi times the square of r.Cheers,