Proof for: area of a sphere = 4.pi.r.squared?

Question

I know the area of a sphere is 4.pi.r.squared. I know this because my daughter's 7th grade math text says so. But how did the world of mathematics come up with that particular formula? How can we prove it, using fundamentals and logic. If the proof is too long to post, can you point me to a reference. Thanks in advance.

Answer 1

There is a short discussion of this, with a diagram, at the internet Math Forum. It multiplied the sphere's circumference by its diameter.

C = 2 pi r.
D = 2r.

(2 pi r)(2r) = 4 pi r².

Answer 2

I assume you mean the *surface* area of a sphere being 4 pi r².

If you were familiar with calculus I could give you a prove using the rotation of a semicircle through space. But that's beyond most 7th graders.

Try the following explanations instead:

Answer 3

4 Pi R Squared

Answer 4

Here is a web page that explains it with a visual...

Answer 5

go to a library