Volume of Spherical Sector given Total Surface Area Calculator

✖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.ⓘ Spherical Radius of Spherical Sector [r_Sphere]			+10% -10%
✖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.ⓘ Total Surface Area of Spherical Sector [TSA]			+10% -10%
✖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.ⓘ Spherical Cap Radius of Spherical Sector [r_Cap]			+10% -10%

✖Volume of Spherical Sector is the amount of three dimensional space occupied by the Spherical Sector.ⓘ Volume of Spherical Sector given Total Surface Area [V]

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Volume of Spherical Sector given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
V = 1/3*pi*r_Sphere^2*(TSA/(pi*r_Sphere)-r_Cap)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Volume of Spherical Sector - (Measured in Cubic Meter) - Volume of Spherical Sector is the amount of three dimensional space occupied by the Spherical Sector.
Spherical Radius of Spherical Sector - (Measured in Meter) - 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.
Total Surface Area of Spherical Sector - (Measured in Square Meter) - 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.
Spherical Cap Radius of Spherical Sector - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Spherical Radius of Spherical Sector: 10 Meter --> 10 Meter No Conversion Required
Total Surface Area of Spherical Sector: 500 Square Meter --> 500 Square Meter No Conversion Required
Spherical Cap Radius of Spherical Sector: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 1/3*pi*r_Sphere^2*(TSA/(pi*r_Sphere)-r_Cap) --> 1/3*pi*10^2*(500/(pi*10)-8)

Evaluating ... ...

V = 828.908625709388

STEP 3: Convert Result to Output's Unit

828.908625709388 Cubic Meter --> No Conversion Required

FINAL ANSWER

828.908625709388 ≈ 828.9086 Cubic Meter <-- Volume of Spherical Sector

(Calculation completed in 00.020 seconds)

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< Volume of Spherical Sector Calculators

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

LaTeX Go 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

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

LaTeX Go 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 given Spherical Cap Radius

LaTeX Go 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 given Surface to Volume Ratio

LaTeX Go Volume of Spherical Sector = 2/3*pi*Spherical Radius of Spherical Sector^2*Spherical Cap Radius of Spherical Sector/((2/3*Spherical Radius of Spherical Sector*Surface to Volume Ratio of Spherical Sector)-2)

Volume of Spherical Sector given Total Surface Area Formula

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What is Spherical Sector?

In geometry, a Spherical Sector, also known as a spherical cone, is a portion of a sphere or of a ball defined by a conical boundary with apex at the center of the sphere. It can be described as the union of a spherical cap and the cone formed by the center of the sphere and the base of the cap. It is the three-dimensional analogue of the sector of a circle.

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

Volume of Spherical Sector given Total Surface Area calculator 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 calculate 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 calculate Volume of Spherical Sector given Total Surface Area using this online calculator? To use this online calculator 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. Here is how the Volume of Spherical Sector given Total Surface Area calculation can be explained with given input values -> 828.9086 = 1/3*pi*10^2*(500/(pi*10)-8).

FAQ

What is Volume of Spherical Sector given Total Surface Area?

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 and is represented as V = 1/3*pi*r_Sphere^2*(TSA/(pi*r_Sphere)-r_Cap) or 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). 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, 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 & 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.

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

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 is calculated using 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 calculate Volume of Spherical Sector given Total Surface Area, you need Spherical Radius of Spherical Sector (r_Sphere), Total Surface Area of Spherical Sector (TSA) & Spherical Cap Radius of Spherical Sector (r_Cap). With our tool, you need to enter the respective value for Spherical Radius of Spherical Sector, Total Surface Area of Spherical Sector & Spherical Cap Radius of Spherical Sector and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Volume of Spherical Sector?

In this formula, Volume of Spherical Sector uses Spherical Radius of Spherical Sector, Total Surface Area of Spherical Sector & Spherical Cap Radius of Spherical Sector. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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