Express the volume of a sphere as a simplified function of its circumference?
- Posted:
- 3+ months ago by Bobby101
- Topics:
- sphere, volume, mathematics, circumference
Responses (3)
circumference c := 2 * pi * r
volume v := 4/3 * pi * r^3
Express v as a function of c: f(c) = v
Obviously the two definitions (of c and v) have the same structure. The main difference is the exponent of r. So, let's cube c:
c^3 = (2 * pi * r)^3 = 8 * pi^3 *r^3.
Now we've settled the transformation for r. Dividing by pi² reduces the exponent of pi to 1. And dividing 8 by 6 yields 4/3. And the combined expression is:
v = f(c) = c^3 / (6 * pi²)
