## Sphere volume - how to calculate it?

The volume of the sphere, as in the case of other geometric figures, is calculated using the established formula. What do we know about the ball and what is the formula? Check it out!

## 1. What is a ball?

The sphere is a three-dimensional geometric solid in space, limited by the so-called the sphere, i.e. the edge (surface) of the sphere. It is made by rotating 360 degrees of a semicircle (or 180 degrees of a circle) around the axis that contains the diameter of that circle (semicircle).

It can also be defined as a set of points that are equal to or shorter than a given length from some point in space. This length is called the radius of the sphere and the selected point is called its center.

Within the sphere we also distinguish a concept such as the ball chord. It is a segment whose ends belong to the surface (edge) of the sphere. The diameter of the ball, as is the case with a circle and a circle, is the chord that passes through the center of the ball. Its length is twice the radius of the sphere.

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Along the entire diameter, the ball varies in width. The axial section of the sphere is the circle. A circle with the radius of this sphere and its center in the center of the sphere is called a great circle. This is the largest circle that we can put into a ball. It divides the sphere into two symmetrical hemispheres.

Interestingly, we can find a great wheel in nature. It will be the equator.

We can write a polyhedron into the sphere if its vertices belong to its sphere. A cone can be entered if the vertex and the circles in the base belong to a sphere. In the case of a cylinder, we can write it into a sphere if the circles in the base also belong to the sphere.

We can also describe a polyhedron on a sphere. This is possible if all faces of the solid are tangent to the sphere. In the case of a cylinder and a cone, if their bases and generators are tangent to the sphere.

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## 2. How to calculate the volume of a sphere - formula

To calculate the volume of a given sphere, we need to know the size of its radius, which we denote r. For the formula we also need Pi - a mathematical constant that equals approximately 3.14159265.

Formula for the volume of a sphere:

V = 4 / 3πr ^ 3

Where V = volume of the sphere and r = radius of the sphere.

## 3. The volume of the sphere - tasks

Excercise 1.

Calculate the volume of the sphere. r = 3 cm.

• a. 21π
• b. 32
• c. 36π

Exercise 2.

The volume of the sphere is equal to V = 32 cm3. Calculate the radius length (r) of the sphere. Use the π≈3 approximation for your calculations.

• a. 3π
• b. 2 cm
• c. 5π