Geometry/Algebra/Calculus

posted by .

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 semi-circle 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 -

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.

Similar Questions

1. math

direct variation the surface area of a sphere varies directly as the square of the radius. if the surface area of a sphere is 36 pi meters squared when the radius is 3 meters, what is the surface area of a sphere with a radius of 6 …
2. Physics

Sphere 1 has surface area A1 and volume V1, and sphere 2 has surface area A2 and volume V2. If the radius of sphere 2 is 3.5 times the radius of sphere 1, what is the ratio of each of the following?
3. mathematics

What is the solution for this? The surface area of a sphere varies in direct proportion to the square of its radius. If a sphere of radius 6cm has a surface area of 452 square cm, find, to the nearest mm, the radius of a spherewith
4. calculus

A hole of a radius of 1cm is pierced in a sphere of a 4cm radius. Calculate the volume of the remaining sphere. I know that the volume of a sphere with an exterior radius is of: V = pie(R^2 - r^2) dH where R^2 is the exterior surface …
5. calculus *improper integrals*

A hole of a radius of 1cm is pierced in a sphere of a 4cm radius. Calculate the volume of the remaining sphere. I know that the volume of a sphere with an exterior radius is of: V = pie(R^2 - r^2) dH where R^2 is the exterior surface …
6. Algebra

A sphere has a radius of 4x + 1. Which polynomial in standard form best describes the total surface area of the sphere?
7. Algebra II

12. A sphere has a radius of 4x + 1. Which polynomial in standard form best describes the total surface area of the sphere?
8. algebra--1 question

A sphere has a radius of 4x + 1. Which polynomial in standard form best describes the total surface area of the sphere?
9. Geometry

#1: A ball has a radius of 1 foot. What is the surface area of the ball?
10. algebra

use 1.9 as the radius for the sphere and answer the following 1-volume = 2-surface area= 3-ratio of the volume to surface area= remember everything is with the sphere and radius 1.9 you have to use them to answer the volume, surface …

More Similar Questions

Post a New Question