Spherical Cap Radius of Spherical Sector given Volume and Spherical Cap Height Calculator

✖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%
✖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 given Volume and Spherical Cap Height [r_Cap]

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Spherical Cap Radius of Spherical Sector given Volume and Spherical Cap Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Spherical Cap Radius of Spherical Sector = sqrt(Spherical Cap Height of Spherical Sector*((2*sqrt((3*Volume of Spherical Sector)/(2*pi*Spherical Cap Height of Spherical Sector)))-Spherical Cap Height of Spherical Sector))
r_Cap = sqrt(h_Cap*((2*sqrt((3*V)/(2*pi*h_Cap)))-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

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.
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.
Volume of Spherical Sector - (Measured in Cubic Meter) - Volume of Spherical Sector is the amount of three dimensional space occupied by the Spherical Sector.

STEP 1: Convert Input(s) to Base Unit

Spherical Cap Height of Spherical Sector: 4 Meter --> 4 Meter No Conversion Required
Volume of Spherical Sector: 840 Cubic Meter --> 840 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_Cap = sqrt(h_Cap*((2*sqrt((3*V)/(2*pi*h_Cap)))-h_Cap)) --> sqrt(4*((2*sqrt((3*840)/(2*pi*4)))-4))

Evaluating ... ...

r_Cap = 8.0066830921109

STEP 3: Convert Result to Output's Unit

8.0066830921109 Meter --> No Conversion Required

FINAL ANSWER

8.0066830921109 ≈ 8.006683 Meter <-- Spherical Cap Radius of Spherical Sector

(Calculation completed in 00.020 seconds)

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< Spherical Cap Radius of Spherical Sector Calculators

Spherical Cap Radius of Spherical Sector given Volume

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

Spherical Cap Radius of Spherical Sector given Surface to Volume Ratio

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

Spherical Cap Radius of Spherical Sector

LaTeX Go Spherical Cap Radius of Spherical Sector = sqrt(Spherical Cap Height of Spherical Sector*((2*Spherical Radius of Spherical Sector)-Spherical Cap Height of Spherical Sector))

Spherical Cap Radius of Spherical Sector given Total Surface Area

LaTeX Go Spherical Cap Radius of Spherical Sector = 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 given Volume and 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 Spherical Cap Radius of Spherical Sector given Volume and Spherical Cap Height?

Spherical Cap Radius of Spherical Sector given Volume and Spherical Cap Height calculator uses Spherical Cap Radius of Spherical Sector = sqrt(Spherical Cap Height of Spherical Sector*((2*sqrt((3*Volume of Spherical Sector)/(2*pi*Spherical Cap Height of Spherical Sector)))-Spherical Cap Height of Spherical Sector)) to calculate the Spherical Cap Radius of Spherical Sector, Spherical Cap Radius of Spherical Sector given Volume and Spherical Cap Height formula is defined as the distance between center and any point on the circumference of the circle at the bottom level of the cap surface of the Spherical Sector, calculated using its volume and spherical cap height. Spherical Cap Radius of Spherical Sector is denoted by r_Cap symbol.

How to calculate Spherical Cap Radius of Spherical Sector given Volume and Spherical Cap Height using this online calculator? To use this online calculator for Spherical Cap Radius of Spherical Sector given Volume and Spherical Cap Height, enter Spherical Cap Height of Spherical Sector (h_Cap) & Volume of Spherical Sector (V) and hit the calculate button. Here is how the Spherical Cap Radius of Spherical Sector given Volume and Spherical Cap Height calculation can be explained with given input values -> 8.006683 = sqrt(4*((2*sqrt((3*840)/(2*pi*4)))-4)).

FAQ

What is Spherical Cap Radius of Spherical Sector given Volume and Spherical Cap Height?

Spherical Cap Radius of Spherical Sector given Volume and Spherical Cap Height formula is defined as the distance between center and any point on the circumference of the circle at the bottom level of the cap surface of the Spherical Sector, calculated using its volume and spherical cap height and is represented as r_Cap = sqrt(h_Cap*((2*sqrt((3*V)/(2*pi*h_Cap)))-h_Cap)) or Spherical Cap Radius of Spherical Sector = sqrt(Spherical Cap Height of Spherical Sector*((2*sqrt((3*Volume of Spherical Sector)/(2*pi*Spherical Cap Height of Spherical Sector)))-Spherical Cap Height of Spherical Sector)). 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 & Volume of Spherical Sector is the amount of three dimensional space occupied by the Spherical Sector.

How to calculate Spherical Cap Radius of Spherical Sector given Volume and Spherical Cap Height?

Spherical Cap Radius of Spherical Sector given Volume and Spherical Cap Height formula is defined as the distance between center and any point on the circumference of the circle at the bottom level of the cap surface of the Spherical Sector, calculated using its volume and spherical cap height is calculated using Spherical Cap Radius of Spherical Sector = sqrt(Spherical Cap Height of Spherical Sector*((2*sqrt((3*Volume of Spherical Sector)/(2*pi*Spherical Cap Height of Spherical Sector)))-Spherical Cap Height of Spherical Sector)). To calculate Spherical Cap Radius of Spherical Sector given Volume and Spherical Cap Height, you need Spherical Cap Height of Spherical Sector (h_Cap) & Volume of Spherical Sector (V). With our tool, you need to enter the respective value for Spherical Cap Height of Spherical Sector & Volume 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 Spherical Cap Radius of Spherical Sector?

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

Spherical Cap Radius of Spherical Sector = sqrt(Spherical Cap Height of Spherical Sector*((2*Spherical Radius of Spherical Sector)-Spherical Cap Height of Spherical Sector))
Spherical Cap Radius of Spherical Sector = 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 = (2*Spherical Radius of Spherical Sector*Spherical Cap Height of Spherical Sector*Surface to Volume Ratio of Spherical Sector)/3-(2*Spherical Cap Height of Spherical Sector)

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