how do i find the volume of a sphere?

Question

i know the formula but i don't undeerstand the 4/3 part
pleases help

Answer 1

Volume of sphere = 4/3 x π x r ³

Answer 2

The derivation of the formula was first accomplished by the Greek mathematician, Archimedes, I believe. What he did was to essentially use a cylinder with radius r and height 2r to show that when a cone shape of radius r and height r is bored into both ends of the cylinder, the remaining volume in each half of the cylinder is equal to half the volume of a sphere with the same radius as the cylinder. Since the volume of a cone with a base of radius r is V(cone) = (1/3) [π r²] h, and, in our particular case, the height, h = (2r/2) = r, then the volume not bored out of each half is:

V(remainder) =
V(½ cylinder) - V(cone) =
π r² (2r)/2 - (1/3) [π r²] (2r)/2 =
π r² r - (1/3) πr² r =
(2/3) π r² r =
(2/3) πr³.

Since there are two halves to the entire cylinder, we multiply the last result above by 2 to obtain:

V(total remainder) = 2(2/3) πr³ = (4/3) πr³.

That's how we come up with (4/3) in the formula for the volume of a sphere.

The reasoning behind Archimedes' conclusion involves the use of what's called Cavalieri's Principle. Cavalieri's Principle states that given two solids of equal height, h, if a plane parallel to the base of each and intersecting each solid at the same arbitrary height, h', where 0 ≤ h' ≤ h, cuts out equal areas in each, then the solids are equal in volume.

Archimedes showed that the area of each slice of the half cylinder after boring out the cone was equal to the area of each slice of the half sphere at every arbitrary height, h'. Therefore, he concluded their volumes were equal.

Answer 3

volume is found by integrating over the area of a circle of the same radius as the sphere under the sphere equation. this is where the 4/3 comes from

Answer 4

Volume of sphere = (4/3) .π. r ³ where r is the radius

Example
If r = 10 cm
V = (4/3).π x 1000 cm³ = 4189 cm³

Answer 5

go to math.glencoe.org and then you will figure out

Answer 6

use pie 3.14