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

✖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 given Volume [TSA]

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Total Surface Area of Spherical Sector given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Spherical Sector = pi*Spherical Radius of Spherical Sector*((3*Volume of Spherical Sector)/(pi*Spherical Radius of Spherical Sector^2)+Spherical Cap Radius of Spherical Sector)
TSA = pi*r_Sphere*((3*V)/(pi*r_Sphere^2)+r_Cap)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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 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.
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 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
Volume of Spherical Sector: 840 Cubic Meter --> 840 Cubic 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

TSA = pi*r_Sphere*((3*V)/(pi*r_Sphere^2)+r_Cap) --> pi*10*((3*840)/(pi*10^2)+8)

Evaluating ... ...

TSA = 503.327412287183

STEP 3: Convert Result to Output's Unit

503.327412287183 Square Meter --> No Conversion Required

FINAL ANSWER

503.327412287183 ≈ 503.3274 Square Meter <-- Total Surface Area of Spherical Sector

(Calculation completed in 00.013 seconds)

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< Total Surface Area of Spherical Sector Calculators

Total Surface Area of Spherical Sector given Spherical Cap Radius

LaTeX Go Total Surface Area 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)+Spherical Cap Radius of Spherical Sector)

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

LaTeX Go Total Surface Area of Spherical Sector = pi*sqrt((3*Volume of Spherical Sector)/(2*pi*Spherical Cap Height of Spherical Sector))*((2*Spherical Cap Height of Spherical Sector)+Spherical Cap Radius of Spherical Sector)

Total Surface Area of Spherical Sector given Surface to Volume Ratio and Spherical Cap Radius

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

Total Surface Area of Spherical Sector

LaTeX Go Total Surface Area of Spherical Sector = pi*Spherical Radius of Spherical Sector*((2*Spherical Cap Height of Spherical Sector)+Spherical Cap Radius of Spherical Sector)

Total Surface Area of Spherical Sector given Volume Formula

LaTeX Go

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 Total Surface Area of Spherical Sector given Volume?

Total Surface Area of Spherical Sector given Volume calculator uses Total Surface Area of Spherical Sector = pi*Spherical Radius of Spherical Sector*((3*Volume of Spherical Sector)/(pi*Spherical Radius of Spherical Sector^2)+Spherical Cap Radius of Spherical Sector) to calculate the Total Surface Area of Spherical Sector, Total Surface Area of Spherical Sector given Volume formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Spherical Sector, calculated using its volume. Total Surface Area of Spherical Sector is denoted by TSA symbol.

How to calculate Total Surface Area of Spherical Sector given Volume using this online calculator? To use this online calculator for Total Surface Area of Spherical Sector given Volume, enter Spherical Radius of Spherical Sector (r_Sphere), Volume of Spherical Sector (V) & Spherical Cap Radius of Spherical Sector (r_Cap) and hit the calculate button. Here is how the Total Surface Area of Spherical Sector given Volume calculation can be explained with given input values -> 503.3274 = pi*10*((3*840)/(pi*10^2)+8).

FAQ

What is Total Surface Area of Spherical Sector given Volume?

Total Surface Area of Spherical Sector given Volume formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Spherical Sector, calculated using its volume and is represented as TSA = pi*r_Sphere*((3*V)/(pi*r_Sphere^2)+r_Cap) or Total Surface Area of Spherical Sector = pi*Spherical Radius of Spherical Sector*((3*Volume of Spherical Sector)/(pi*Spherical Radius of Spherical Sector^2)+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, Volume of Spherical Sector is the amount of three dimensional space occupied by 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 Total Surface Area of Spherical Sector given Volume?

Total Surface Area of Spherical Sector given Volume formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Spherical Sector, calculated using its volume is calculated using Total Surface Area of Spherical Sector = pi*Spherical Radius of Spherical Sector*((3*Volume of Spherical Sector)/(pi*Spherical Radius of Spherical Sector^2)+Spherical Cap Radius of Spherical Sector). To calculate Total Surface Area of Spherical Sector given Volume, you need Spherical Radius of Spherical Sector (r_Sphere), Volume of Spherical Sector (V) & Spherical Cap Radius of Spherical Sector (r_Cap). With our tool, you need to enter the respective value for Spherical Radius of Spherical Sector, Volume 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 Total Surface Area of Spherical Sector?

In this formula, Total Surface Area of Spherical Sector uses Spherical Radius of Spherical Sector, Volume 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 -

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

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