Jul 28, 2014 · 48 I was looking for proofs using Calculus for the area of a circle and come across this one $$\int 2 \pi r \, dr = 2\pi \frac {r^2} {2} = \pi r^2$$ and it struck me as being particularly …

Feb 12, 2020 · HINT.-In the attached figure you can calculate the intersection point $P$ and the angles $a$ and $b$. You know the area of a circular sector $OPR$ is given by $\dfrac …

The circumference of a sphere (measured along the arc) is $2 \pi r,$ so then the surface area of a sphere should be $\pi (\pi r)^2 = \pi^3 r^2$ (here, the radius of the circle is half the …

What would you set the limits if you need to calculate the area of an infinitesimal ring in cartesian coordinates i.e. $\int dx \int dy $.. where you only want to integrate on the infinitesimal ring..

4 There's a classic trick to do this with just elementary geometry: The green region is a triangle, and the shaded region is a circular wedge: both have standard formulas for their area. To find …

Apr 29, 2011 · the diameters differ by 9cm, so if the inner circle has radius r, the outer circle has radius r + 4.5. The area of the crescent is the difference in the areas of the circles: pi (r + …

2 I am trying to calculate the area of a specific region inside a circle. The region, in this case, is the green area inside the circle. The given material is the equation, radius and the center of …

Nov 21, 2018 · The second part is an estimate of square dies on the edge of the circle. This is estimated by counting number of squares that can be layed along the edge of circle so that …

I know how to integrate and deduce the area of a circle using vertical "slices" (dx). However, I wanted to know how to solve the problem another way: slicing the circle like one would slice a …

Suppose you have 2 circles that intersect each other in such a way that each circle passes through the other's center. What is the area between the circle (or common area) i.e. area …