areacirclesgeometryintegration
I'm sorry maybe it's obvious but English is not my first language. I just want to know what is asked in this question:
The area of a circle (in square inches) is numerically larger than its circumference (in inches). What is the smallest possible integral area of the circle, in square inches?
Specifically I don't understand what integral area means. I'm familiar with integration and how you can calculate the area between the curve and the axes but what should the integral area of a circle mean?
From the Wikipedia article Area of a disk:
Once you know the circumference of a circle with radius $r$ is $2\pi r$, you can use what is described in the image to approximate the area of the circle by a parallelogram with height $r$ and base $\pi r$.
The circle fits snuggly between one pair of parallels, but is two large for the other pair. It follows that the diameter of the circle is the larger of the two distances between parallels (aka. altidudes). In other words, the diameter of the circle is $4\,\text{cm}$ and the height of the shaded region is the difference $4\,\text{cm}-3\,\text{cm}=1\,\text{cm}$. Can you take it from here?
Best Answer
Most likely, "integral" means "is an integer". The area of this circle, expressed in square inches, is an integer.