Volume of Spherical Segment given Total Surface Area and Radius Calculator

✖Total Surface Area of Spherical Segment is the quantity of plane enclosed on the entire surface of the Spherical Segment.ⓘ Total Surface Area of Spherical Segment [TSA]			+10% -10%
✖Base Radius of Spherical Segment is a radial line from the center to any point on the circumference of the base of the Spherical Segment.ⓘ Base Radius of Spherical Segment [r_Base]			+10% -10%
✖Top Radius of Spherical Segment is a radial line from the center to any point on the circumference of the top base of a Spherical Segment.ⓘ Top Radius of Spherical Segment [r_Top]			+10% -10%
✖Radius of Spherical Segment is the line segment extending from the center to the circumference of Sphere in which Spherical Segment is bounded.ⓘ Radius of Spherical Segment [r]			+10% -10%

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

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Volume of Spherical Segment given Total Surface Area and Radius

Formula

`"V" = ("TSA"-(pi*("r"_{"Base"}^2+"r"_{"Top"}^2)))/(12*"r")*(3*"r"_{"Top"}^2+3*"r"_{"Base"}^2+(("TSA"-(pi*("r"_{"Base"}^2+"r"_{"Top"}^2)))/(2*pi*"r"))^2)`

Example

`"1356.431m³"=("830m²"-(pi*(("10m")^2+("8m")^2)))/(12*"10m")*(3*("8m")^2+3*("10m")^2+(("830m²"-(pi*(("10m")^2+("8m")^2)))/(2*pi*"10m"))^2)`

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Volume of Spherical Segment given Total Surface Area and Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Spherical Segment = (Total Surface Area of Spherical Segment-(pi*(Base Radius of Spherical Segment^2+Top Radius of Spherical Segment^2)))/(12*Radius of Spherical Segment)*(3*Top Radius of Spherical Segment^2+3*Base Radius of Spherical Segment^2+((Total Surface Area of Spherical Segment-(pi*(Base Radius of Spherical Segment^2+Top Radius of Spherical Segment^2)))/(2*pi*Radius of Spherical Segment))^2)
V = (TSA-(pi*(r_Base^2+r_Top^2)))/(12*r)*(3*r_Top^2+3*r_Base^2+((TSA-(pi*(r_Base^2+r_Top^2)))/(2*pi*r))^2)
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Volume of Spherical Segment - (Measured in Cubic Meter) - Volume of Spherical Segment is the amount of three dimensional space occupied by the Spherical Segment.
Total Surface Area of Spherical Segment - (Measured in Square Meter) - Total Surface Area of Spherical Segment is the quantity of plane enclosed on the entire surface of the Spherical Segment.
Base Radius of Spherical Segment - (Measured in Meter) - Base Radius of Spherical Segment is a radial line from the center to any point on the circumference of the base of the Spherical Segment.
Top Radius of Spherical Segment - (Measured in Meter) - Top Radius of Spherical Segment is a radial line from the center to any point on the circumference of the top base of a Spherical Segment.
Radius of Spherical Segment - (Measured in Meter) - Radius of Spherical Segment is the line segment extending from the center to the circumference of Sphere in which Spherical Segment is bounded.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Spherical Segment: 830 Square Meter --> 830 Square Meter No Conversion Required
Base Radius of Spherical Segment: 10 Meter --> 10 Meter No Conversion Required
Top Radius of Spherical Segment: 8 Meter --> 8 Meter No Conversion Required
Radius of Spherical Segment: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (TSA-(pi*(r_Base^2+r_Top^2)))/(12*r)*(3*r_Top^2+3*r_Base^2+((TSA-(pi*(r_Base^2+r_Top^2)))/(2*pi*r))^2) --> (830-(pi*(10^2+8^2)))/(12*10)*(3*8^2+3*10^2+((830-(pi*(10^2+8^2)))/(2*pi*10))^2)

Evaluating ... ...

V = 1356.43092293945

STEP 3: Convert Result to Output's Unit

1356.43092293945 Cubic Meter --> No Conversion Required

FINAL ANSWER

1356.43092293945 ≈ 1356.431 Cubic Meter <-- Volume of Spherical Segment

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 3D Geometry » Spherical Segment » Volume of Spherical Segment » Volume of Spherical Segment given Total Surface Area and Radius

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< 3 Volume of Spherical Segment Calculators

Volume of Spherical Segment given Total Surface Area and Radius

Go Volume of Spherical Segment = (Total Surface Area of Spherical Segment-(pi*(Base Radius of Spherical Segment^2+Top Radius of Spherical Segment^2)))/(12*Radius of Spherical Segment)*(3*Top Radius of Spherical Segment^2+3*Base Radius of Spherical Segment^2+((Total Surface Area of Spherical Segment-(pi*(Base Radius of Spherical Segment^2+Top Radius of Spherical Segment^2)))/(2*pi*Radius of Spherical Segment))^2)

Volume of Spherical Segment given Center to Base and Top to Top Radius Length

Go Volume of Spherical Segment = 1/2*pi*(Radius of Spherical Segment-Center to Base Radius Length of Spherical Segment-Top to Top Radius Length of Spherical Segment)*(Top Radius of Spherical Segment^2+Base Radius of Spherical Segment^2+(Radius of Spherical Segment-Center to Base Radius Length of Spherical Segment-Top to Top Radius Length of Spherical Segment)^2/3)

Volume of Spherical Segment

Go Volume of Spherical Segment = 1/2*pi*Height of Spherical Segment*(Top Radius of Spherical Segment^2+Base Radius of Spherical Segment^2+Height of Spherical Segment^2/3)

Volume of Spherical Segment given Total Surface Area and Radius Formula

What is Spherical Segment?

In geometry, a Spherical Segment is the solid defined by cutting a sphere with a pair of parallel planes . It can be thought of as a spherical cap with the top truncated, and so it corresponds to a spherical frustum.

How to Calculate Volume of Spherical Segment given Total Surface Area and Radius?

Volume of Spherical Segment given Total Surface Area and Radius calculator uses Volume of Spherical Segment = (Total Surface Area of Spherical Segment-(pi*(Base Radius of Spherical Segment^2+Top Radius of Spherical Segment^2)))/(12*Radius of Spherical Segment)*(3*Top Radius of Spherical Segment^2+3*Base Radius of Spherical Segment^2+((Total Surface Area of Spherical Segment-(pi*(Base Radius of Spherical Segment^2+Top Radius of Spherical Segment^2)))/(2*pi*Radius of Spherical Segment))^2) to calculate the Volume of Spherical Segment, Volume of Spherical Segment given Total Surface Area and Radius formula is defined as the amount of three dimensional space occupied by the Spherical Segment, and calculated using the total surface area and radius of Spherical Segment. Volume of Spherical Segment is denoted by V symbol.

How to calculate Volume of Spherical Segment given Total Surface Area and Radius using this online calculator? To use this online calculator for Volume of Spherical Segment given Total Surface Area and Radius, enter Total Surface Area of Spherical Segment (TSA), Base Radius of Spherical Segment (r_Base), Top Radius of Spherical Segment (r_Top) & Radius of Spherical Segment (r) and hit the calculate button. Here is how the Volume of Spherical Segment given Total Surface Area and Radius calculation can be explained with given input values -> 1356.431 = (830-(pi*(10^2+8^2)))/(12*10)*(3*8^2+3*10^2+((830-(pi*(10^2+8^2)))/(2*pi*10))^2).

FAQ

What is Volume of Spherical Segment given Total Surface Area and Radius?

Volume of Spherical Segment given Total Surface Area and Radius formula is defined as the amount of three dimensional space occupied by the Spherical Segment, and calculated using the total surface area and radius of Spherical Segment and is represented as V = (TSA-(pi*(r_Base^2+r_Top^2)))/(12*r)*(3*r_Top^2+3*r_Base^2+((TSA-(pi*(r_Base^2+r_Top^2)))/(2*pi*r))^2) or Volume of Spherical Segment = (Total Surface Area of Spherical Segment-(pi*(Base Radius of Spherical Segment^2+Top Radius of Spherical Segment^2)))/(12*Radius of Spherical Segment)*(3*Top Radius of Spherical Segment^2+3*Base Radius of Spherical Segment^2+((Total Surface Area of Spherical Segment-(pi*(Base Radius of Spherical Segment^2+Top Radius of Spherical Segment^2)))/(2*pi*Radius of Spherical Segment))^2). Total Surface Area of Spherical Segment is the quantity of plane enclosed on the entire surface of the Spherical Segment, Base Radius of Spherical Segment is a radial line from the center to any point on the circumference of the base of the Spherical Segment, Top Radius of Spherical Segment is a radial line from the center to any point on the circumference of the top base of a Spherical Segment & Radius of Spherical Segment is the line segment extending from the center to the circumference of Sphere in which Spherical Segment is bounded.

How to calculate Volume of Spherical Segment given Total Surface Area and Radius?

Volume of Spherical Segment given Total Surface Area and Radius formula is defined as the amount of three dimensional space occupied by the Spherical Segment, and calculated using the total surface area and radius of Spherical Segment is calculated using Volume of Spherical Segment = (Total Surface Area of Spherical Segment-(pi*(Base Radius of Spherical Segment^2+Top Radius of Spherical Segment^2)))/(12*Radius of Spherical Segment)*(3*Top Radius of Spherical Segment^2+3*Base Radius of Spherical Segment^2+((Total Surface Area of Spherical Segment-(pi*(Base Radius of Spherical Segment^2+Top Radius of Spherical Segment^2)))/(2*pi*Radius of Spherical Segment))^2). To calculate Volume of Spherical Segment given Total Surface Area and Radius, you need Total Surface Area of Spherical Segment (TSA), Base Radius of Spherical Segment (r_Base), Top Radius of Spherical Segment (r_Top) & Radius of Spherical Segment (r). With our tool, you need to enter the respective value for Total Surface Area of Spherical Segment, Base Radius of Spherical Segment, Top Radius of Spherical Segment & Radius of Spherical Segment 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 Segment?

In this formula, Volume of Spherical Segment uses Total Surface Area of Spherical Segment, Base Radius of Spherical Segment, Top Radius of Spherical Segment & Radius of Spherical Segment. We can use 2 other way(s) to calculate the same, which is/are as follows -

Volume of Spherical Segment = 1/2*pi*Height of Spherical Segment*(Top Radius of Spherical Segment^2+Base Radius of Spherical Segment^2+Height of Spherical Segment^2/3)
Volume of Spherical Segment = 1/2*pi*(Radius of Spherical Segment-Center to Base Radius Length of Spherical Segment-Top to Top Radius Length of Spherical Segment)*(Top Radius of Spherical Segment^2+Base Radius of Spherical Segment^2+(Radius of Spherical Segment-Center to Base Radius Length of Spherical Segment-Top to Top Radius Length of Spherical Segment)^2/3)

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