How do you did they come up with the formula to find the surface area and the volume for a sphere.?

Question

in a sphere surface area and volume
surface area=4*pi*radius to the power of two
volume=4/3*pi*radius*to the power of two

How did they come up with the formula to find the surface area and the volume for a sphere.?
in a sphere surface area and volume
surface area=4*pi*radius to the power of two
volume=4/3*pi*radius*to the power of two

Answer 1

This is a fantastic question. Many people are willing to accept any formula without justification. The answer is that it can be shown using calculus. If you're not there yet, then detailing the proofs would probably not be helpful, although I'm sure you can find them online. The volume should be easier to show than the surface area. One last note: I would be remiss not to point out that your volume formula is missing a power on r.

Answer 2

If you can find the area of a circle, you can find the area of a half-circle and calculate the volume of a sphere by rotation.

Once you know the volume, you can find the surface area by taking the derivative. (4/3)*pi*r^3 -> 4pi*r^2

Answer 3

i'm undecided what you mean via "the place each and each section comes from", in case you mean like a length * width * top answer. the only variable in a sphere is its radius. the rest, 4 and pi are constants. in case you're asking "how did somebody arise with the floor part of a sphere", it incredibly is incredibly the area of calculus, yet one rapid answer is that in case you have 2 spheres that are close mutually in length, and seem on the fee of exchange of quantity with comprehend to radius, if V = 4/3 pi r^3, the by-product is dV = 4 pi r^2, which seems to be the floor section, yet it incredibly is not a evidence, and not a frequently valid thank you to get floor section. frequently you approximate floor section with closer and closer approximations which tend to attain 4 * pi * r^2. (r = radius)