Total Surface Area of Spherical Sector given Spherical Cap Height 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%
✖Spherical Cap Height of Spherical Sector is the vertical distance from the topmost point to the bottom level of the cap surface of the Spherical Sector.ⓘ Spherical Cap Height of Spherical Sector [h_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 Spherical Cap Height [TSA]

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Total Surface Area of Spherical Sector given Spherical Cap Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Spherical Sector = pi*Spherical Radius of Spherical Sector*((2*Spherical Cap Height of Spherical Sector)+sqrt(Spherical Cap Height of Spherical Sector*((2*Spherical Radius of Spherical Sector)-Spherical Cap Height of Spherical Sector)))
TSA = pi*r_Sphere*((2*h_Cap)+sqrt(h_Cap*((2*r_Sphere)-h_Cap)))
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

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.
Spherical Cap Height of Spherical Sector - (Measured in Meter) - Spherical Cap Height of Spherical Sector is the vertical distance from the topmost point to 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
Spherical Cap Height of Spherical Sector: 4 Meter --> 4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = pi*r_Sphere*((2*h_Cap)+sqrt(h_Cap*((2*r_Sphere)-h_Cap))) --> pi*10*((2*4)+sqrt(4*((2*10)-4)))

Evaluating ... ...

TSA = 502.654824574367

STEP 3: Convert Result to Output's Unit

502.654824574367 Square Meter --> No Conversion Required

FINAL ANSWER

502.654824574367 ≈ 502.6548 Square Meter <-- Total Surface Area of Spherical Sector

(Calculation completed in 00.004 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 Spherical Cap Height 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 Spherical Cap Height?

Total Surface Area of Spherical Sector given Spherical Cap Height calculator uses Total Surface Area of Spherical Sector = pi*Spherical Radius of Spherical Sector*((2*Spherical Cap Height of Spherical Sector)+sqrt(Spherical Cap Height of Spherical Sector*((2*Spherical Radius of Spherical Sector)-Spherical Cap Height of Spherical Sector))) to calculate the Total Surface Area of Spherical Sector, Total Surface Area of Spherical Sector given Spherical Cap Height formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Spherical Sector, calculated using its spherical cap height. Total Surface Area of Spherical Sector is denoted by TSA symbol.

How to calculate Total Surface Area of Spherical Sector given Spherical Cap Height using this online calculator? To use this online calculator for Total Surface Area of Spherical Sector given Spherical Cap Height, enter Spherical Radius of Spherical Sector (r_Sphere) & Spherical Cap Height of Spherical Sector (h_Cap) and hit the calculate button. Here is how the Total Surface Area of Spherical Sector given Spherical Cap Height calculation can be explained with given input values -> 502.6548 = pi*10*((2*4)+sqrt(4*((2*10)-4))).

FAQ

What is Total Surface Area of Spherical Sector given Spherical Cap Height?

Total Surface Area of Spherical Sector given Spherical Cap Height formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Spherical Sector, calculated using its spherical cap height and is represented as TSA = pi*r_Sphere*((2*h_Cap)+sqrt(h_Cap*((2*r_Sphere)-h_Cap))) or Total Surface Area of Spherical Sector = pi*Spherical Radius of Spherical Sector*((2*Spherical Cap Height of Spherical Sector)+sqrt(Spherical Cap Height of Spherical Sector*((2*Spherical Radius of Spherical Sector)-Spherical Cap Height 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 & Spherical Cap Height of Spherical Sector is the vertical distance from the topmost point to the bottom level of the cap surface of the Spherical Sector.

How to calculate Total Surface Area of Spherical Sector given Spherical Cap Height?

Total Surface Area of Spherical Sector given Spherical Cap Height formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Spherical Sector, calculated using its spherical cap height is calculated using Total Surface Area of Spherical Sector = pi*Spherical Radius of Spherical Sector*((2*Spherical Cap Height of Spherical Sector)+sqrt(Spherical Cap Height of Spherical Sector*((2*Spherical Radius of Spherical Sector)-Spherical Cap Height of Spherical Sector))). To calculate Total Surface Area of Spherical Sector given Spherical Cap Height, you need Spherical Radius of Spherical Sector (r_Sphere) & Spherical Cap Height of Spherical Sector (h_Cap). With our tool, you need to enter the respective value for Spherical Radius of Spherical Sector & Spherical Cap Height 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 & Spherical Cap Height 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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