Why is the surface area of a Sphere 4pi times radius squared???

Описание: You might have memorized that the surface area of a sphere of radius a is 4 pi a^2. But why? In this video we will compute it using the surface area formula we came up with in the previous video. First, we will parametrize the surface using spherical coordinates with a fixed radius. Second, we will plug it into the surface area formula for parameterized surfaces that we derived in the previous video in the playlist (see below). At this point it is just computational to compute the length of the cross product and evaluate the resulting double integral.

Note that this video is quite computational, it doesn't shed any light into the geometry of why this makes sense, it just says we get this result when we plug into the formulas we derived previously. For a more geometric view interpretting this as 4 times the shadow of pi*radius^2 check out the 3blue1brown video here:    • But why is a sphere's surface area four ti...  

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