Height of Spherical Cap given Cap Radius Calculator

✖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%
✖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%

✖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 Cap Radius [h]

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Height of Spherical Cap given Cap Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Spherical Cap = Sphere Radius of Spherical Cap-sqrt(Sphere Radius of Spherical Cap^2-Cap Radius of Spherical Cap^2)
h = r_Sphere-sqrt(r_Sphere^2-r_Cap^2)
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

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.
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.
Cap Radius of Spherical Cap - (Measured in Meter) - Cap Radius of Spherical Cap is the radius of the base circle of a Spherical Cap.

STEP 1: Convert Input(s) to Base Unit

Sphere Radius of Spherical Cap: 10 Meter --> 10 Meter No Conversion Required
Cap Radius of Spherical Cap: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = r_Sphere-sqrt(r_Sphere^2-r_Cap^2) --> 10-sqrt(10^2-8^2)

Evaluating ... ...

h = 4

STEP 3: Convert Result to Output's Unit

4 Meter --> No Conversion Required

FINAL ANSWER

4 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 Cap Radius Formula

LaTeX Go

Height of Spherical Cap = Sphere Radius of Spherical Cap-sqrt(Sphere Radius of Spherical Cap^2-Cap Radius of Spherical Cap^2)
h = r_Sphere-sqrt(r_Sphere^2-r_Cap^2)

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 Cap Radius?

Height of Spherical Cap given Cap Radius calculator uses Height of Spherical Cap = Sphere Radius of Spherical Cap-sqrt(Sphere Radius of Spherical Cap^2-Cap Radius of Spherical Cap^2) to calculate the Height of Spherical Cap, Height of Spherical Cap given 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 cap radius and sphere radius of the Spherical Cap. Height of Spherical Cap is denoted by h symbol.

How to calculate Height of Spherical Cap given Cap Radius using this online calculator? To use this online calculator for Height of Spherical Cap given Cap Radius, enter Sphere Radius of Spherical Cap (r_Sphere) & Cap Radius of Spherical Cap (r_Cap) and hit the calculate button. Here is how the Height of Spherical Cap given Cap Radius calculation can be explained with given input values -> 4 = 10-sqrt(10^2-8^2).

FAQ

What is Height of Spherical Cap given Cap Radius?

Height of Spherical Cap given 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 cap radius and sphere radius of the Spherical Cap and is represented as h = r_Sphere-sqrt(r_Sphere^2-r_Cap^2) or Height of Spherical Cap = Sphere Radius of Spherical Cap-sqrt(Sphere Radius of Spherical Cap^2-Cap Radius of Spherical Cap^2). Sphere Radius of Spherical Cap is the radius of the sphere from which the Spherical Cap shape is cut & Cap Radius of Spherical Cap is the radius of the base circle of a Spherical Cap.

How to calculate Height of Spherical Cap given Cap Radius?

Height of Spherical Cap given 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 cap radius and sphere radius of the Spherical Cap is calculated using Height of Spherical Cap = Sphere Radius of Spherical Cap-sqrt(Sphere Radius of Spherical Cap^2-Cap Radius of Spherical Cap^2). To calculate Height of Spherical Cap given Cap Radius, you need Sphere Radius of Spherical Cap (r_Sphere) & Cap Radius of Spherical Cap (r_Cap). With our tool, you need to enter the respective value for Sphere Radius of Spherical Cap & Cap 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 Sphere Radius of Spherical Cap & Cap Radius of Spherical Cap. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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