# Circumference of a sphere – Circumference of a Sphere — Definition, Formula, Equation & Examples

Содержание

## Sphere Calculator

### Sphere Shape

V = volume
A = surface area
C = circumference
π = pi = 3.14159
√ = square root

### Calculator Use

This online calculator will calculate the 3 unknown values of a sphere given any 1 known variable including radius r, surface area A, volume V and circumference C. A sphere is a set of points in three dimensional space that are located at an equal distance r (the radius) from a given point (the center point).

* Units: Note that units are shown for convenience but do not affect the calculations. The units are in place to give an indication of the order of the results such as ft, ft2 or ft3. For example, if you are starting with mm and you know r in mm, your calculations will result with A in mm2, V in mm3 and C in mm.

### Sphere Formulas in terms of radius r:

• Volume of a sphere:
• Circumference of a sphere:
• Surface area of a sphere:

Volume of a Sphere

$V = \frac{4}{3}\pi r^3$

$V \approx 4.1888r^3$

$V = \frac{A^{3/2}}{6\sqrt{\pi}}$

$V \approx 0.09403A^{3/2}$

$V = \frac{C^3}{6\pi^2}$

$V \approx 0.01689C^3$

Surface Area of a Sphere

$A = 4 \pi r^2$

$A \approx 12.5664r^2$

$A = \pi^{1/3} (6V)^{2/3}$

$A \approx 4.83598V^{2/3}$

$A = \frac{C^2}{\pi}$

$A \approx 0.3183C^2$

$r = \left(\frac{3V}{4 \pi}\right)^{1/3}$

$r \approx 0.62035V^{1/3}$

$r = \sqrt{\frac{A}{4 \pi}}$

$r \approx 0.2821 \sqrt{A}$

$r = \frac{C}{2 \pi}$

$r \approx 0.1592C$

Circumference of a Sphere

$C = 2 \pi r$

$C \approx 6.2832r$

$C = \pi^{2/3} (6V)^{1/3}$

$C \approx 3.89778V^{1/3}$

$C = \sqrt{\pi A}$

$C \approx 1.77245\sqrt{A}$

#### 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
• Given the volume of a sphere calculate the radius, surface area and circumference
Given V find r, A, C
• Given the surface area of a sphere calculate the radius, volume and circumference
Given A find r, V, C
• Given the circumference of a sphere calculate the radius, volume and surface area
Given C find r, V, A

www.calculatorsoup.com

## circumference of sphere — это… Что такое circumference of sphere?

• Circumference — Cir*cum fer*ence, n. [L. circumferentia.] [1913 Webster] 1. The line that goes round or encompasses a circular figure; a periphery. Millon. [1913 Webster] 2. A circle; anything circular. [1913 Webster] His ponderous shield . . . Behind him cast.… …   The Collaborative International Dictionary of English

• sphere — sphereless, adj. spherelike, adj. /sfear/, n., v., sphered, sphering. n. 1. Geom. a. a solid geometric figure generated by the revolution of a semicircle about its diameter; a round body whose surface is at all points equidistant from the center …   Universalium

• Sphere-world — The idea of a sphere world was constructed by Henri Poincaré while pursuing his argument for conventionalism (see philosophy of space and time), offered a thought experiment about a sphere with strange properties.Poincaré asks us to imagine a… …   Wikipedia

• Circle of the sphere — Circle Cir cle (s[ e]r k l), n. [OE. cercle, F. cercle, fr. L. circulus (Whence also AS. circul), dim. of circus circle, akin to Gr. kri kos, ki rkos, circle, ring. Cf. {Circus}, {Circum }.] [1913 Webster] 1. A plane figure, bounded by a single… …   The Collaborative International Dictionary of English

• n-sphere — 2 sphere wireframe as an orthogonal projection Just as a …   Wikipedia

• Bernal sphere — External view of a Bernal sphere The inside of …   Wikipedia

• Dyson Sphere —    An artificial world which is a hollow sphere built around a sun. This allows all of the sun s energy to be used by the inhabitants of the sphere, who live on the inside surface, giving them virtually unlimited energy. The circumference of the… …   The writer’s dictionary of science fiction, fantasy, horror and mythology

• ambit — amÂ·bit || Ã¦mbÉªt n. circumference, limit, sphere, field …   English contemporary dictionary

• Spherical Earth — Medieval artistic representation of a spherical Earth with compartments representing earth, air, and water (c. 1400). The concept of a spherical Earth dates back to ancient Greek philosophy from around the 6th century BC …   Wikipedia

• Flat Earth — For other uses, see Flat Earth (disambiguation). The Flammarion engraving (1888) depicts a traveller who arrives at the edge of a flat Earth and sticks his head through the firmament …   Wikipedia

• analysis — /euh nal euh sis/, n., pl. analyses / seez /. 1. the separating of any material or abstract entity into its constituent elements (opposed to synthesis). 2. this process as a method of studying the nature of something or of determining its… …   Universalium

## circumference, surface area, enclosed volume of sphere (formula and on-line calculator)

#### Calculation

Enter a value to any field — the others are calculated themselves. If you change a value in any field, the others are automatically recalculated.

For decimals you can enter either points or commas
as decimal marks (but only one decimal point in a value).

The result will be in the units that you enter into the fields.

For example: if you enter kilometres, calculation will be also in kilometres.

If appears an error NaN, check whether you enter to the field
a correct value, ie. without any letters and other characters.

#### Formula

 Diameter d = 2 × r [m] Circumference O = π × d = 2 × π × r [m] Surface area P = π × d² = 4 × π × r² [m²] Enclosed volume V = 1/6 π × d³ = 4/3 π × r³ [m³]

d … diameter = 2 × radius

r … radius = ½ of diameter

S … center of sphere

o … axis

#### Sphere and Cube

Space/volume diagonal of cube (u3) = diameter of circumscribed sphere

Length of side edge of cube (a) = diameter of inscribed sphere

#### How to calculate …

Bold shapes and objects are already in operation. The others contain only a formula.

#### You might be interested

sphere.wikina.org

## circumference of sphere — это… Что такое circumference of sphere?

• Circumference — Cir*cum fer*ence, n. [L. circumferentia.] [1913 Webster] 1. The line that goes round or encompasses a circular figure; a periphery. Millon. [1913 Webster] 2. A circle; anything circular. [1913 Webster] His ponderous shield . . . Behind him cast.… …   The Collaborative International Dictionary of English

• sphere — sphereless, adj. spherelike, adj. /sfear/, n., v., sphered, sphering. n. 1. Geom. a. a solid geometric figure generated by the revolution of a semicircle about its diameter; a round body whose surface is at all points equidistant from the center …   Universalium

• Sphere-world — The idea of a sphere world was constructed by Henri Poincaré while pursuing his argument for conventionalism (see philosophy of space and time), offered a thought experiment about a sphere with strange properties.Poincaré asks us to imagine a… …   Wikipedia

• Circle of the sphere — Circle Cir cle (s[ e]r k l), n. [OE. cercle, F. cercle, fr. L. circulus (Whence also AS. circul), dim. of circus circle, akin to Gr. kri kos, ki rkos, circle, ring. Cf. {Circus}, {Circum }.] [1913 Webster] 1. A plane figure, bounded by a single… …   The Collaborative International Dictionary of English

• n-sphere — 2 sphere wireframe as an orthogonal projection Just as a …   Wikipedia

• Bernal sphere — External view of a Bernal sphere The inside of …   Wikipedia

• Dyson Sphere —    An artificial world which is a hollow sphere built around a sun. This allows all of the sun s energy to be used by the inhabitants of the sphere, who live on the inside surface, giving them virtually unlimited energy. The circumference of the… …   The writer’s dictionary of science fiction, fantasy, horror and mythology

• ambit — amÂ·bit || Ã¦mbÉªt n. circumference, limit, sphere, field …   English contemporary dictionary

• Spherical Earth — Medieval artistic representation of a spherical Earth with compartments representing earth, air, and water (c. 1400). The concept of a spherical Earth dates back to ancient Greek philosophy from around the 6th century BC …   Wikipedia

• Flat Earth — For other uses, see Flat Earth (disambiguation). The Flammarion engraving (1888) depicts a traveller who arrives at the edge of a flat Earth and sticks his head through the firmament …   Wikipedia

• analysis — /euh nal euh sis/, n., pl. analyses / seez /. 1. the separating of any material or abstract entity into its constituent elements (opposed to synthesis). 2. this process as a method of studying the nature of something or of determining its… …   Universalium

## Q: Is it a coincidence that a circles circumference is the derivative of its area, as well as the volume of a sphere being the antiderivative of its surface area? What is the explanation for this?

Physicist: For those of you not hip to the calculus groove, here’s what’s going down:  The derivative of Y with respect to X, written , is just a description of how fast Y changes when X changes.  It so happens that if , then .  So, for example, if , then .  The area of a circle is , and the circumference is , which is the derivative.  The volume of a sphere is , and the surface area is , which is again the derivative.  This, it turns out, is no coincidence!

If you describe volume, V, in terms of the radius, R, then increasing R will result in an increase in V that’s proportional to the surface area. If the surface area is given by S(R), then you’ll find that for a tiny change in the radius, dR, , or .

You can think of a sphere as a series of very thin surfaces added together.  This is another, equivalent, way of describing the situation.  Each layer adds (surface area of layer)x(thickness of layer) to the volume.

You can think of this like painting a spherical tank. The increase in volume, dV, is the amount of paint you use, and the amount of paint is just the surface area, S(R), times the thickness of the paint, dR.  This same argument can be used to show that the volume is the integral of the surface area (just keep painting layer after layer).

It’s a little easier to keep track of what’s going on with circles.

If you increase the radius of a circle by a tiny amount, dR, then the area increases by (2πR)(dR).

The same “derivative thing” holds up for the circumference vs. the area of a circle.  The change in area, dA, is dA = (2πR)dR.  So, .  That is, the derivative of the area is just the circumference.

This, by the way, is one of the arguments for using “τ” instead of “π”. τ = 2π, so the area of a circle is . This makes the “differential nature” of the circumference a little more obvious.

Answer gravy: By the way, this argument is only exact when the thickness of the new layer “goes to zero“.  Basically, the top of the new layer is a little longer/bigger than the bottom of the new layer.  So if the area is , and the change in radius is , then

This extra little is a result of the top and bottom of the new layer being very slightly different lengths.  But when ΔR is small, (ΔR)2 is really small.  For example, if ΔR is one thousandth, then (ΔR)2 is one millionth.  The whole idea behind calculus is that when the scales get very small you can just ignore these “extra tiny” terms.  In fact, this is the essential difference between dA and ΔA, and how the derivative is defined:

## circumference of sphere — это… Что такое circumference of sphere?

• Circumference — Cir*cum fer*ence, n. [L. circumferentia.] [1913 Webster] 1. The line that goes round or encompasses a circular figure; a periphery. Millon. [1913 Webster] 2. A circle; anything circular. [1913 Webster] His ponderous shield . . . Behind him cast.… …   The Collaborative International Dictionary of English

• sphere — sphereless, adj. spherelike, adj. /sfear/, n., v., sphered, sphering. n. 1. Geom. a. a solid geometric figure generated by the revolution of a semicircle about its diameter; a round body whose surface is at all points equidistant from the center …   Universalium

• Sphere-world — The idea of a sphere world was constructed by Henri Poincaré while pursuing his argument for conventionalism (see philosophy of space and time), offered a thought experiment about a sphere with strange properties.Poincaré asks us to imagine a… …   Wikipedia

• Circle of the sphere — Circle Cir cle (s[ e]r k l), n. [OE. cercle, F. cercle, fr. L. circulus (Whence also AS. circul), dim. of circus circle, akin to Gr. kri kos, ki rkos, circle, ring. Cf. {Circus}, {Circum }.] [1913 Webster] 1. A plane figure, bounded by a single… …   The Collaborative International Dictionary of English

• n-sphere — 2 sphere wireframe as an orthogonal projection Just as a …   Wikipedia

• Bernal sphere — External view of a Bernal sphere The inside of …   Wikipedia

• Dyson Sphere —    An artificial world which is a hollow sphere built around a sun. This allows all of the sun s energy to be used by the inhabitants of the sphere, who live on the inside surface, giving them virtually unlimited energy. The circumference of the… …   The writer’s dictionary of science fiction, fantasy, horror and mythology

• ambit — amÂ·bit || Ã¦mbÉªt n. circumference, limit, sphere, field …   English contemporary dictionary

• Spherical Earth — Medieval artistic representation of a spherical Earth with compartments representing earth, air, and water (c. 1400). The concept of a spherical Earth dates back to ancient Greek philosophy from around the 6th century BC …   Wikipedia

• Flat Earth — For other uses, see Flat Earth (disambiguation). The Flammarion engraving (1888) depicts a traveller who arrives at the edge of a flat Earth and sticks his head through the firmament …   Wikipedia

• analysis — /euh nal euh sis/, n., pl. analyses / seez /. 1. the separating of any material or abstract entity into its constituent elements (opposed to synthesis). 2. this process as a method of studying the nature of something or of determining its… …   Universalium

## circumference of sphere — это… Что такое circumference of sphere?

• Circumference — Cir*cum fer*ence, n. [L. circumferentia.] [1913 Webster] 1. The line that goes round or encompasses a circular figure; a periphery. Millon. [1913 Webster] 2. A circle; anything circular. [1913 Webster] His ponderous shield . . . Behind him cast.… …   The Collaborative International Dictionary of English

• sphere — sphereless, adj. spherelike, adj. /sfear/, n., v., sphered, sphering. n. 1. Geom. a. a solid geometric figure generated by the revolution of a semicircle about its diameter; a round body whose surface is at all points equidistant from the center …   Universalium

• Sphere-world — The idea of a sphere world was constructed by Henri Poincaré while pursuing his argument for conventionalism (see philosophy of space and time), offered a thought experiment about a sphere with strange properties.Poincaré asks us to imagine a… …   Wikipedia

• Circle of the sphere — Circle Cir cle (s[ e]r k l), n. [OE. cercle, F. cercle, fr. L. circulus (Whence also AS. circul), dim. of circus circle, akin to Gr. kri kos, ki rkos, circle, ring. Cf. {Circus}, {Circum }.] [1913 Webster] 1. A plane figure, bounded by a single… …   The Collaborative International Dictionary of English

• n-sphere — 2 sphere wireframe as an orthogonal projection Just as a …   Wikipedia

• Bernal sphere — External view of a Bernal sphere The inside of …   Wikipedia

• Dyson Sphere —    An artificial world which is a hollow sphere built around a sun. This allows all of the sun s energy to be used by the inhabitants of the sphere, who live on the inside surface, giving them virtually unlimited energy. The circumference of the… …   The writer’s dictionary of science fiction, fantasy, horror and mythology

• ambit — amÂ·bit || Ã¦mbÉªt n. circumference, limit, sphere, field …   English contemporary dictionary

• Spherical Earth — Medieval artistic representation of a spherical Earth with compartments representing earth, air, and water (c. 1400). The concept of a spherical Earth dates back to ancient Greek philosophy from around the 6th century BC …   Wikipedia

• Flat Earth — For other uses, see Flat Earth (disambiguation). The Flammarion engraving (1888) depicts a traveller who arrives at the edge of a flat Earth and sticks his head through the firmament …   Wikipedia

• analysis — /euh nal euh sis/, n., pl. analyses / seez /. 1. the separating of any material or abstract entity into its constituent elements (opposed to synthesis). 2. this process as a method of studying the nature of something or of determining its… …   Universalium