Spherical segment volume calculator

From ancient times, people needed to measure the amount of various substances. Bulk substances and liquids could be measured by filling them with vessels of a certain capacity, determining their quantity by volume. The concept of volume in solid geometry is introduced similarly to the concept of area in plane geometry. In plane geometry, we determined the area like this: the area of ​​a polygon is the value of the part of the plane that the polygon occupies. To formulate the concept of volume similarly to this concept. The magnitude of the part of the space occupied by the geometric body is called the volume of this body. Volume is measured in "cubic" units.

Spherical segment — the surface, part of the sphere, cut off from it by a distinct plane. A plane cuts off two parts: a smaller section is also called a spherical cap or spherical dome. If the plane passes through the center of the sphere, so that the height of both segments is equal to the radius of the sphere, then such spherical segments are called a hemisphere.

A spherical segment is a part of a sphere that is cut off by a plane. The volume of a spherical segment can be calculated using the following formula:

V = \pi h^2 \left( R - \dfrac{h}{3} \right)

Where V is the volume, h is the height of the segment, and r is the radius of the sphere.

To make it easy for you to find the volume of your spherical segment, we've created a calculator for you to use. Simply enter the values of h and r below, and our calculator will automatically give you the volume.

How to Use the Spherical Segment Volume Calculator

1. Enter the value of h in the first box.
2. Enter the value of r in the second box.
3. The calculator will automatically calculate the volume of your spherical segment.

Spherical Segment Volume Formula Examples

Here are some examples of finding the volume of a spherical segment using the formula:

Example 1:

Find the volume of a spherical segment with a height of 8 cm and a radius of 5 cm.

V = (1/3) * pi * 8^2 * (3*5 - 8) = 179.61 cm^3

Example 2:

Find the volume of a spherical segment with a height of 2 cm and a radius of 7 cm.

V = (1/3) * pi * 2^2 * (3*7 - 2) = 146.14 cm^3

Conclusion

Calculating the volume of a spherical segment is an important skill in mathematics. Our spherical segment volume calculator and formula make it easy to find the volume of your spherical segment. Try it out for yourself and see how easy it can be!