Answer:
r = radius
V = volume
A = surface area
C = circumference
π = pi = 3.1415926535898
√ = square root
Sphere Formulas in terms of radius r:
Volume of a sphere:
V = (4/3)πr3
Circumference of a sphere:
C = 2πr
Surface area of a sphere:
A = 4πr2
Volume of a Sphere
in terms of
radius \[ V = \frac{4}{3}\pi r^3 \] \[ V \approx 4.1888r^3 \]
in terms of
surface area \[ V = \frac{A^{3/2}}{6\sqrt{\pi}} \] \[ V \approx 0.09403A^{3/2} \]
in terms of
circumference \[ V = \frac{C^3}{6\pi^2} \] \[ V \approx 0.01689C^3 \]
Surface Area of a Sphere
in terms of
radius \[ A = 4 \pi r^2 \] \[ A \approx 12.5664r^2 \]
in terms of
volume \[ A = \pi^{1/3} (6V)^{2/3} \] \[ A \approx 4.83598V^{2/3} \]
in terms of
circumference \[ A = \frac{C^2}{\pi} \] \[ A \approx 0.3183C^2 \]
Radius of a Sphere
in terms of
volume \[ r = \left(\frac{3V}{4 \pi}\right)^{1/3} \] \[ r \approx 0.62035V^{1/3} \]
in terms of
surface area \[ r = \sqrt{\frac{A}{4 \pi}} \] \[ r \approx 0.2821 \sqrt{A} \]
in terms of
circumference \[ r = \frac{C}{2 \pi} \] \[ r \approx 0.1592C \]
Circumference of a Sphere
in terms of
radius \[ C = 2 \pi r \] \[ C \approx 6.2832r \]
in terms of
volume \[ C = \pi^{2/3} (6V)^{1/3} \] \[ C \approx 3.89778V^{1/3} \]
in terms of
surface area \[ C = \sqrt{\pi A} \] \[ C \approx 1.77245\sqrt{A} \]
Sphere Calculations:
Use the following additional formulas along with the formulas above.
Given the radius of a sphere calculate the volume, surface area and circumference
Given r find V, A, C
use the formulas above
Given the volume of a sphere calculate the radius, surface area and circumference
Given V find r, A, C
r = cube root(3V / 4π)
Given the surface area of a sphere calculate the radius, volume and circumference
Given A find r, V, C
r = √(A / 4π)
Given the circumference of a sphere calculate the radius, volume and surface area
Given C find r, V, A
r = C / 2π
