Question

Work out the volume of this sphere. leave your answer in terms of pi

Answer 1

Volume is = (4/3) πr

Answer 2

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