Surface to Volume Ratio of Spherical Sector 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%
✖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%

✖Surface to Volume Ratio of Spherical Sector is defined as the numerical ratio of the total surface area of a Spherical Sector to the volume of the Spherical Sector.ⓘ Surface to Volume Ratio of Spherical Sector [R_A/V]

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Surface to Volume Ratio of Spherical Sector Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface to Volume Ratio 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)))/(2*Spherical Radius of Spherical Sector*Spherical Cap Height of Spherical Sector/3)
R_A/V = ((2*h_Cap)+sqrt(h_Cap*((2*r_Sphere)-h_Cap)))/(2*r_Sphere*h_Cap/3)
This formula uses 1 Functions, 3 Variables

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

Surface to Volume Ratio of Spherical Sector - (Measured in 1 per Meter) - Surface to Volume Ratio of Spherical Sector is defined as the numerical ratio of the total surface area of a Spherical Sector to the volume 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.
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.

STEP 1: Convert Input(s) to Base Unit

Spherical Cap Height of Spherical Sector: 4 Meter --> 4 Meter No Conversion Required
Spherical Radius of Spherical Sector: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = ((2*h_Cap)+sqrt(h_Cap*((2*r_Sphere)-h_Cap)))/(2*r_Sphere*h_Cap/3) --> ((2*4)+sqrt(4*((2*10)-4)))/(2*10*4/3)

Evaluating ... ...

R_A/V = 0.6

STEP 3: Convert Result to Output's Unit

0.6 1 per Meter --> No Conversion Required

FINAL ANSWER

0.6 1 per Meter <-- Surface to Volume Ratio of Spherical Sector

(Calculation completed in 00.008 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< Surface to Volume Ratio of Spherical Sector Calculators

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

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

Surface to Volume Ratio of Spherical Sector

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

Surface to Volume Ratio of Spherical Sector given Spherical Cap Radius

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

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

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

Surface to Volume Ratio of Spherical Sector 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 Surface to Volume Ratio of Spherical Sector?

Surface to Volume Ratio of Spherical Sector calculator uses Surface to Volume Ratio 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)))/(2*Spherical Radius of Spherical Sector*Spherical Cap Height of Spherical Sector/3) to calculate the Surface to Volume Ratio of Spherical Sector, Surface to Volume Ratio of Spherical Sector formula is defined as the numerical ratio of the total surface area of a Spherical Sector to the volume of the Spherical Sector. Surface to Volume Ratio of Spherical Sector is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Spherical Sector using this online calculator? To use this online calculator for Surface to Volume Ratio of Spherical Sector, enter Spherical Cap Height of Spherical Sector (h_Cap) & Spherical Radius of Spherical Sector (r_Sphere) and hit the calculate button. Here is how the Surface to Volume Ratio of Spherical Sector calculation can be explained with given input values -> 0.6 = ((2*4)+sqrt(4*((2*10)-4)))/(2*10*4/3).

FAQ

What is Surface to Volume Ratio of Spherical Sector?

Surface to Volume Ratio of Spherical Sector formula is defined as the numerical ratio of the total surface area of a Spherical Sector to the volume of the Spherical Sector and is represented as R_A/V = ((2*h_Cap)+sqrt(h_Cap*((2*r_Sphere)-h_Cap)))/(2*r_Sphere*h_Cap/3) or Surface to Volume Ratio 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)))/(2*Spherical Radius of Spherical Sector*Spherical Cap Height of Spherical Sector/3). 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 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.

How to calculate Surface to Volume Ratio of Spherical Sector?

Surface to Volume Ratio of Spherical Sector formula is defined as the numerical ratio of the total surface area of a Spherical Sector to the volume of the Spherical Sector is calculated using Surface to Volume Ratio 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)))/(2*Spherical Radius of Spherical Sector*Spherical Cap Height of Spherical Sector/3). To calculate Surface to Volume Ratio of Spherical Sector, you need Spherical Cap Height of Spherical Sector (h_Cap) & Spherical Radius of Spherical Sector (r_Sphere). With our tool, you need to enter the respective value for Spherical Cap Height of Spherical Sector & Spherical 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 Surface to Volume Ratio of Spherical Sector?

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

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

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