Posted by John on Sunday, January 26, 2014 at 1:46am.
Why isn't the surface area of a sphere with radius r the following:
2*pi * (pi*r)
That comes from the following flow of logic:
Doesn't it makes sense to think of the surface area of the sphere with radius r as the the circumference of the semicircle with radius r, pi*r (2*pi*r/2 = pi*r), multiplied by 2*pi, effectively "rotating" the semicircle along an orthogonal angular axis 2*pi radians (360 degrees)? In my mind, that would "trace" the surface area of a sphere, wouldn't it? What am I missing / not seeing?
Thanks

Geometry/Algebra/Calculus  Steve, Sunday, January 26, 2014 at 6:37am
the problem is, that to rotate a curve, there has to be a variable radius of rotation. You have the 2pi, but don't specify what the radius of rotation is.
area needs to be in square units, but you only have r once, a linear unit.
Answer This Question
Related Questions
 calculus *improper integrals*  A hole of a radius of 1cm is pierced in a sphere...
 math  direct variation the surface area of a sphere varies directly as the ...
 calculus  A hole of a radius of 1cm is pierced in a sphere of a 4cm radius. ...
 Physics  Sphere 1 has surface area A1 and volume V1, and sphere 2 has surface ...
 Algebra II  12. A sphere has a radius of 4x + 1. Which polynomial in standard ...
 algebra1 question  A sphere has a radius of 4x + 1. Which polynomial in ...
 Algebra  A sphere has a radius of 4x + 1. Which polynomial in standard form ...
 mathematics  What is the solution for this? The surface area of a sphere varies...
 algebra  use 1.9 as the radius for the sphere and answer the following 1volume...
 math  A solid cone of height 12cm and radius 9 cm is recast into a solid sphere...
More Related Questions