The formula of the volume and area of \u200b\u200bthe full surface of the ball, sphere through the radius and the diameter of the ball: value. Examples of calculating the surface area and volume of the ball, through the radius and diameter of the ball: description. How to find the volume of the ball through the surface area of \u200b\u200bthe ball: Example

The article will be useful to schoolchildren and future applicants who are preparing for the exam.

Formula of the volume of the ball through the radius: meaning

The volume of the ball V is calculated by the formula (see below), where R is the radius of the ball, the number “pi” - π is a mathematical constant, ≈ 3.14.

This formula is the base!

Formula of the volume of the ball through the diameter: value

1. Use the base formula: V \u003d 4/3*π*r³.
2. Radius R is ½ diameter d or r \u003d d/2.
3. Hence: v \u003d 4/3*π*r³ → v \u003d (4π/3)*(d/2) ³ → v \u003d (4π/3)*(d³/8) → V \u003d πD.³/6.

Or

Examples of calculating the volume of the ball, through the radius and the diameter of the ball: Description

Task 1.

The radius of the ball is 10 cm. Find its volume.

Task 2.

The diameter of the ball is 10 cm. Find its volume.

Task 3.

The ratio of the diameter of the moon and the diameter of the Earth 1: 4. How many times the volume of the Earth is greater than the volume of the moon?

Solution:

Answer: 64 times.

Important: There are many online calculators that allow you to quickly find a given value. For example, service Webmath.

Formula of the full surface of the ball, sphere through the radius: meaning

The surface area of \u200b\u200bthe sphere/ball s is calculated by the formula (see below), where R is the radius of the ball, the number “pi” - π is a mathematical constant, ≈ 3.14.

This formula is the base!

The formula of the full surface of the ball, sphere through the diameter: value

1. Use the base formula: S \u003d 4*π*r².
2. Radius R is ½ diameter d or r \u003d d/2.
3. From here: S \u003d 4*π*r² → S \u003d 4*π*(d/2) ² → S \u003d (4π)*(D²/4) → S \u003d (4πd²)/4 → S \u003d πD.².

Or

Examples of calculating the surface area, sphere of the ball, through the radius and diameter of the ball: Description

Task 4.

Task 5.

Task 6.

How to find the volume of the ball through the surface area of \u200b\u200bthe ball, sphere: an example of solving a problem

Task 7.

Task 8.

Video: USE Mathematics. The volume and area of \u200b\u200bthe surface of the bodies of rotation.