Height of Spherical Cap given Total Surface Area and Cap Radius Calculator

✖Total Surface Area of Spherical Cap is the total quantity of two dimensional space enclosed on the base and curved surfaces of the Spherical Cap.ⓘ Total Surface Area of Spherical Cap [TSA]			+10% -10%
✖Cap Radius of Spherical Cap is the radius of the base circle of a Spherical Cap.ⓘ Cap Radius of Spherical Cap [r_Cap]			+10% -10%
✖Sphere Radius of Spherical Cap is the radius of the sphere from which the Spherical Cap shape is cut.ⓘ Sphere Radius of Spherical Cap [r_Sphere]			+10% -10%

✖Height of Spherical Cap is the maximum vertical distance from the base circle to the curved surface of the Spherical Cap.ⓘ Height of Spherical Cap given Total Surface Area and Cap Radius [h]

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Height of Spherical Cap given Total Surface Area and Cap Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Spherical Cap = (Total Surface Area of Spherical Cap-(pi*Cap Radius of Spherical Cap^2))/(2*pi*Sphere Radius of Spherical Cap)
h = (TSA-(pi*r_Cap^2))/(2*pi*r_Sphere)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Height of Spherical Cap - (Measured in Meter) - Height of Spherical Cap is the maximum vertical distance from the base circle to the curved surface of the Spherical Cap.
Total Surface Area of Spherical Cap - (Measured in Square Meter) - Total Surface Area of Spherical Cap is the total quantity of two dimensional space enclosed on the base and curved surfaces of the Spherical Cap.
Cap Radius of Spherical Cap - (Measured in Meter) - Cap Radius of Spherical Cap is the radius of the base circle of a Spherical Cap.
Sphere Radius of Spherical Cap - (Measured in Meter) - Sphere Radius of Spherical Cap is the radius of the sphere from which the Spherical Cap shape is cut.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Spherical Cap: 450 Square Meter --> 450 Square Meter No Conversion Required
Cap Radius of Spherical Cap: 8 Meter --> 8 Meter No Conversion Required
Sphere Radius of Spherical Cap: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = (TSA-(pi*r_Cap^2))/(2*pi*r_Sphere) --> (450-(pi*8^2))/(2*pi*10)

Evaluating ... ...

h = 3.96197243913529

STEP 3: Convert Result to Output's Unit

3.96197243913529 Meter --> No Conversion Required

FINAL ANSWER

3.96197243913529 ≈ 3.961972 Meter <-- Height of Spherical Cap

(Calculation completed in 00.004 seconds)

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< Height of Spherical Cap Calculators

Height of Spherical Cap given Total Surface Area and Cap Radius

LaTeX Go Height of Spherical Cap = (Total Surface Area of Spherical Cap-(pi*Cap Radius of Spherical Cap^2))/(2*pi*Sphere Radius of Spherical Cap)

Height of Spherical Cap given Cap Radius

LaTeX Go Height of Spherical Cap = Sphere Radius of Spherical Cap-sqrt(Sphere Radius of Spherical Cap^2-Cap Radius of Spherical Cap^2)

Height of Spherical Cap given Curved Surface Area

LaTeX Go Height of Spherical Cap = Curved Surface Area of Spherical Cap/(2*pi*Sphere Radius of Spherical Cap)

Height of Spherical Cap given Total Surface Area and Cap Radius Formula

LaTeX Go

Height of Spherical Cap = (Total Surface Area of Spherical Cap-(pi*Cap Radius of Spherical Cap^2))/(2*pi*Sphere Radius of Spherical Cap)
h = (TSA-(pi*r_Cap^2))/(2*pi*r_Sphere)

What is a Spherical Cap?

In geometry, a Spherical Cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i.e., bounded by a single plane. If the plane passes through the center of the sphere, so that the height of the cap is equal to the radius of the sphere, the Spherical Cap is called a hemisphere.

How to Calculate Height of Spherical Cap given Total Surface Area and Cap Radius?

Height of Spherical Cap given Total Surface Area and Cap Radius calculator uses Height of Spherical Cap = (Total Surface Area of Spherical Cap-(pi*Cap Radius of Spherical Cap^2))/(2*pi*Sphere Radius of Spherical Cap) to calculate the Height of Spherical Cap, Height of Spherical Cap given Total Surface Area and Cap Radius formula is defined as the maximum vertical distance from the base circle to the curved surface of the Spherical Cap, and calculated using the total surface area, sphere radius and cap radius of the Spherical Cap. Height of Spherical Cap is denoted by h symbol.

How to calculate Height of Spherical Cap given Total Surface Area and Cap Radius using this online calculator? To use this online calculator for Height of Spherical Cap given Total Surface Area and Cap Radius, enter Total Surface Area of Spherical Cap (TSA), Cap Radius of Spherical Cap (r_Cap) & Sphere Radius of Spherical Cap (r_Sphere) and hit the calculate button. Here is how the Height of Spherical Cap given Total Surface Area and Cap Radius calculation can be explained with given input values -> 3.961972 = (450-(pi*8^2))/(2*pi*10).

FAQ

What is Height of Spherical Cap given Total Surface Area and Cap Radius?

Height of Spherical Cap given Total Surface Area and Cap Radius formula is defined as the maximum vertical distance from the base circle to the curved surface of the Spherical Cap, and calculated using the total surface area, sphere radius and cap radius of the Spherical Cap and is represented as h = (TSA-(pi*r_Cap^2))/(2*pi*r_Sphere) or Height of Spherical Cap = (Total Surface Area of Spherical Cap-(pi*Cap Radius of Spherical Cap^2))/(2*pi*Sphere Radius of Spherical Cap). Total Surface Area of Spherical Cap is the total quantity of two dimensional space enclosed on the base and curved surfaces of the Spherical Cap, Cap Radius of Spherical Cap is the radius of the base circle of a Spherical Cap & Sphere Radius of Spherical Cap is the radius of the sphere from which the Spherical Cap shape is cut.

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

Height of Spherical Cap given Total Surface Area and Cap Radius formula is defined as the maximum vertical distance from the base circle to the curved surface of the Spherical Cap, and calculated using the total surface area, sphere radius and cap radius of the Spherical Cap is calculated using Height of Spherical Cap = (Total Surface Area of Spherical Cap-(pi*Cap Radius of Spherical Cap^2))/(2*pi*Sphere Radius of Spherical Cap). To calculate Height of Spherical Cap given Total Surface Area and Cap Radius, you need Total Surface Area of Spherical Cap (TSA), Cap Radius of Spherical Cap (r_Cap) & Sphere Radius of Spherical Cap (r_Sphere). With our tool, you need to enter the respective value for Total Surface Area of Spherical Cap, Cap Radius of Spherical Cap & Sphere Radius of Spherical Cap 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 Height of Spherical Cap?

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

Height of Spherical Cap = Sphere Radius of Spherical Cap-sqrt(Sphere Radius of Spherical Cap^2-Cap Radius of Spherical Cap^2)
Height of Spherical Cap = Curved Surface Area of Spherical Cap/(2*pi*Sphere Radius of Spherical Cap)

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