# Tag: area

## geometry – Is the blue area greater than the red area?

The Question : 133 people think this question is useful Problem: A vertex of one square is pegged to the centre of an identical square, and the overlapping area is blue. One of the squares is then rotated about the vertex and the resulting overlap is red. Which area is greater? Let the area of

## geometry – V.I. Arnold says Russian students can’t solve this problem, but American students can — why?

The Question : 273 people think this question is useful In a book of word problems by V.I Arnold, the following appears: The hypotenuse of a right-angled triangle (in a standard American examination) is 10 inches, the altitude dropped onto it is 6 inches. Find the area of the triangle. American school students had been

## alculus – Area covered by a constant length segment rotating around the center of a square.

The Question : 63 people think this question is useful This is an idea I have had in my head for years and years and I would like to know the answer, and also I would like to know if it’s somehow relevant to anything or useless. I describe my thoughts with the following image:

## alculus – Why is the derivative of a circle’s area its perimeter (and similarly for spheres)?

The Question : 109 people think this question is useful When differentiated with respect to $r$, the derivative of $\pi r^2$ is $2 \pi r$, which is the circumference of a circle. Similarly, when the formula for a sphere’s volume $\frac{4}{3} \pi r^3$ is differentiated with respect to $r$, we get $4 \pi r^2$. Is