﻿ Spherical cap: - on line calculation, formula - FORMIAX ﻿

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# Spherical cap - area and volume

A =  π. (q2 + 2.r.h)

V = 1/3.π.h2.(3r – h)

A = Area

V = volume

h = height

## WHAT IS IT ?

A spherical cap is a portion of a sphere that is cut off by a plane. The properties of a spherical cap include:

- Radius (r): The radius of the sphere from which the cap is derived.
- Height (h): The perpendicular distance from the base of the cap (the circular cross-section) to the top of the cap.

Spherical caps are commonly found in various applications in mathematics, engineering, and design, especially in the construction of domes and other curved structures.

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## CALCULATION:

Enter unit e.g.: inch

Enter the number of decimal places

## EXAMPLE:

The radius of the sphere is 5 cm. The height of the spherical cap is 2 cm and the radius of the base of the cap is 3 cm. What is the area and volume of the spherical cap?

Surface area:

Using the formula A = 2πrv + πq², we substitute the values:

A = 2 * 3.14 * 5 * 2 + 3.14 * 3²;

A = 6.28 * 10 + 3.14 * 9;

A = 62.8 + 28.26

A = 91.06 cm²

Volume:

Using the formula V = πv / 6 * (3ρ² + v²), we substitute the values:

V = ((3.14 * 2) / 6) * (3 * 3² + 2²);

V = (6.28 / 6) * (3 * 9 + 4);

V = 1.04666 * 31

V = 32.46 cm³

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