Uses Pi = 3.14159265359 for precise calculations.
A sphere is a perfectly round three-dimensional object where every point on its surface is equidistant from its center. Common examples include balls, globes, and planets.
The volume of a sphere is calculated as:
V = (4/3) * Pi * r^3
The surface area of a sphere is:
A = 4 * Pi * r^2
d = 2r
From Volume: r = cuberoot(3V / (4 * Pi)) From Surface Area: r = sqrt(A / (4 * Pi))
The volume formula comes from calculus - integrating circular cross-sections. The (4/3) factor appears because a sphere can be thought of as composed of infinitely many infinitesimally thin circular disks stacked together.
The surface area is exactly 4 times the area of a circle with the same radius. This is because a sphere can be "unwrapped" to cover exactly 4 circles of radius r.
Given radius = 5 units:
Volume = (4/3) * Pi * 5^3
= (4/3) * Pi * 125
= 166.67 * Pi
= 523.6 cubic units
Surface Area = 4 * Pi * 5^2
= 4 * Pi * 25
= 100 * Pi
= 314.16 square units
Given diameter = 10 units:
Radius = 10 / 2 = 5 units Volume = (4/3) * Pi * 5^3 = 523.6 cubic units Surface Area = 4 * Pi * 5^2 = 314.16 square units
Given volume = 100 cubic units:
r = cuberoot(3 * 100 / (4 * Pi)) r = cuberoot(300 / 12.566) r = cuberoot(23.87) r = 2.88 units
Calculating volumes of atoms, cells, planets, and stars.
Designing spherical tanks, ball bearings, and pressure vessels.
Manufacturing balls for various sports (basketball, soccer, tennis, golf).
Determining how much paint for a spherical object, or water volume in a spherical tank.