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Volume of Spherical Sector given Total Surface Area Formula

GoVolume of Spherical Sector given Spherical Cap Radius Formula

GoVolume of Spherical Sector given Total Surface Area and Spherical Cap Height Formula

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Volume of Spherical Sector is the amount of three dimensional space occupied by the Spherical Sector. Check FAQs

V = \frac{1}{3} \cdot π \cdot {r Sphere}^{2} \cdot (\frac{TSA}{π \cdot r Sphere} - r Cap)

V - Volume of Spherical Sector?r_Sphere - Spherical Radius of Spherical Sector?TSA - Total Surface Area of Spherical Sector?r_Cap - Spherical Cap Radius of Spherical Sector?π - Archimedes' constant?

Volume of Spherical Sector given Total Surface Area Example

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Here is how the Volume of Spherical Sector given Total Surface Area equation looks like with Values.

Here is how the Volume of Spherical Sector given Total Surface Area equation looks like with Units.

Here is how the Volume of Spherical Sector given Total Surface Area equation looks like.

828.9086 = \frac{1}{3} \cdot 3.1416 \cdot 10^{2} \cdot (\frac{500}{3.1416 \cdot 10} - 8)

828.9086m³ = \frac{1}{3} \cdot 3.1416 \cdot {10m}^{2} \cdot (\frac{500m²}{3.1416 \cdot 10m} - 8m)

828.9086 = \frac{1}{3} \cdot 3.1416 \cdot 10^{2} \cdot (\frac{500}{3.1416 \cdot 10} - 8)

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Volume of Spherical Sector given Total Surface Area Solution

Follow our step by step solution on how to calculate Volume of Spherical Sector given Total Surface Area?

FIRST Step Consider the formula

V = \frac{1}{3} \cdot π \cdot {r Sphere}^{2} \cdot (\frac{TSA}{π \cdot r Sphere} - r Cap)

Next Step Substitute values of Variables

∴

V = \frac{1}{3} \cdot π \cdot {10m}^{2} \cdot (\frac{500m²}{π \cdot 10m} - 8m)

Next Step Substitute values of Constants

∴

V = \frac{1}{3} \cdot 3.1416 \cdot {10m}^{2} \cdot (\frac{500m²}{3.1416 \cdot 10m} - 8m)

Next Step Prepare to Evaluate

∴

V = \frac{1}{3} \cdot 3.1416 \cdot 10^{2} \cdot (\frac{500}{3.1416 \cdot 10} - 8)

Next Step Evaluate

∴

V = 828.908625709388m³

LAST Step Rounding Answer

∴

V = 828.9086m³

Volume of Spherical Sector given Total Surface Area Formula Elements

Variables

Constants

Volume of Spherical Sector

Volume of Spherical Sector is the amount of three dimensional space occupied by the Spherical Sector.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Spherical Sector

Spherical Radius of Spherical Sector

Spherical Radius of Spherical Sector is the distance from centre to any point on the surface of the sphere from which the Spherical Sector is cut.

Symbol: r_Sphere

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Spherical Radius of Spherical Sector

Total Surface Area of Spherical Sector

Total Surface Area of Spherical Sector is defined as the total quantity of two-dimensional space enclosed on the entire surface of the Spherical Sector.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Spherical Sector

Spherical Cap Radius of Spherical Sector

Spherical Cap Radius of Spherical Sector is defined as the distance between centre and any point on the circumference of the circle at the bottom level of the cap surface of the Spherical Sector.

Symbol: r_Cap

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Spherical Cap Radius of Spherical Sector

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Volume of Spherical Sector

Go Volume of Spherical Sector given Spherical Cap Radius

V = \frac{π}{2} \cdot {(\frac{{r Cap}^{2}}{h Cap} + h Cap)}^{2} \cdot \frac{h Cap}{3}

Go Volume of Spherical Sector given Total Surface Area and Spherical Cap Height

V = 2 \cdot π \cdot {(\frac{TSA}{π \cdot ((2 \cdot h Cap) + r Cap)})}^{2} \cdot \frac{h Cap}{3}

Go Volume of Spherical Sector given Surface to Volume Ratio and Spherical Cap Height

V = 2 \cdot π \cdot {(\frac{(2 \cdot h Cap) + r Cap}{2 \cdot \frac{h Cap}{3} \cdot R A/V})}^{2} \cdot \frac{h Cap}{3}

Go Volume of Spherical Sector given Surface to Volume Ratio

V = \frac{2}{3} \cdot π \cdot {r Sphere}^{2} \cdot \frac{r Cap}{(\frac{2}{3} \cdot r Sphere \cdot R A/V) - 2}

How to Evaluate Volume of Spherical Sector given Total Surface Area?

Volume of Spherical Sector given Total Surface Area evaluator uses Volume of Spherical Sector = 1/3*pi*Spherical Radius of Spherical Sector^2*(Total Surface Area of Spherical Sector/(pi*Spherical Radius of Spherical Sector)-Spherical Cap Radius of Spherical Sector) to evaluate the Volume of Spherical Sector, Volume of Spherical Sector given Total Surface Area formula is defined as amount of three dimensional space occupied by the Spherical Sector, calculated using its total surface area. Volume of Spherical Sector is denoted by V symbol.

How to evaluate Volume of Spherical Sector given Total Surface Area using this online evaluator? To use this online evaluator for Volume of Spherical Sector given Total Surface Area, enter Spherical Radius of Spherical Sector (r_Sphere), Total Surface Area of Spherical Sector (TSA) & Spherical Cap Radius of Spherical Sector (r_Cap) and hit the calculate button.

FAQs on Volume of Spherical Sector given Total Surface Area

What is the formula to find Volume of Spherical Sector given Total Surface Area?

The formula of Volume of Spherical Sector given Total Surface Area is expressed as Volume of Spherical Sector = 1/3*pi*Spherical Radius of Spherical Sector^2*(Total Surface Area of Spherical Sector/(pi*Spherical Radius of Spherical Sector)-Spherical Cap Radius of Spherical Sector). Here is an example- 828.9086 = 1/3*pi*10^2*(500/(pi*10)-8).

How to calculate Volume of Spherical Sector given Total Surface Area?

With Spherical Radius of Spherical Sector (r_Sphere), Total Surface Area of Spherical Sector (TSA) & Spherical Cap Radius of Spherical Sector (r_Cap) we can find Volume of Spherical Sector given Total Surface Area using the formula - Volume of Spherical Sector = 1/3*pi*Spherical Radius of Spherical Sector^2*(Total Surface Area of Spherical Sector/(pi*Spherical Radius of Spherical Sector)-Spherical Cap Radius of Spherical Sector). This formula also uses Archimedes' constant .

What are the other ways to Calculate Volume of Spherical Sector?

Here are the different ways to Calculate Volume of Spherical Sector-

Volume of Spherical Sector=pi/2*((Spherical Cap Radius of Spherical Sector^2)/Spherical Cap Height of Spherical Sector+Spherical Cap Height of Spherical Sector)^2*Spherical Cap Height of Spherical Sector/3
Volume of Spherical Sector=2*pi*(Total Surface Area of Spherical Sector/(pi*((2*Spherical Cap Height of Spherical Sector)+Spherical Cap Radius of Spherical Sector)))^2*Spherical Cap Height of Spherical Sector/3
Volume of Spherical Sector=2*pi*(((2*Spherical Cap Height of Spherical Sector)+Spherical Cap Radius of Spherical Sector)/(2*Spherical Cap Height of Spherical Sector/3*Surface to Volume Ratio of Spherical Sector))^2*Spherical Cap Height of Spherical Sector/3

Can the Volume of Spherical Sector given Total Surface Area be negative?

No, the Volume of Spherical Sector given Total Surface Area, measured in Volume cannot be negative.

Which unit is used to measure Volume of Spherical Sector given Total Surface Area?

Volume of Spherical Sector given Total Surface Area is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Volume of Spherical Sector given Total Surface Area can be measured.

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Volume of Spherical Sector given Total Surface Area Formula

​GoVolume of Spherical Sector given Spherical Cap Radius Formula

​GoVolume of Spherical Sector given Total Surface Area and Spherical Cap Height Formula

Volume of Spherical Sector given Total Surface Area Example

Volume of Spherical Sector given Total Surface Area Solution

Volume of Spherical Sector given Total Surface Area Formula Elements

Other Formulas to find Volume of Spherical Sector

How to Evaluate Volume of Spherical Sector given Total Surface Area?

FAQs on Volume of Spherical Sector given Total Surface Area

Variable Name

GoVolume of Spherical Sector given Spherical Cap Radius Formula

GoVolume of Spherical Sector given Total Surface Area and Spherical Cap Height Formula