Finding the surface area of ​​a ball (sphere): formula and tasks

In this publication, we will look at how you can find the area of ​​a ball (sphere) and analyze examples of solving problems to fix the material.

Formula for calculating the area of ​​a ball / sphere

1. Through the radius

The area (S) of the surface of a ball/sphere is equal to the product of its four radii squared and the number π.

S = 4 π R²

Note: in calculations the value of the number π rounded up to 3,14.

2. Through diameter

As you know, the diameter of a ball/sphere is equal to two of its radii: d = 2R. Therefore, you can calculate the surface area of ​​uXNUMXbuXNUMXba figure using this kind of formula:

S = 4 π (d/2)²

Examples of tasks

Task 1

Calculate the surface area of ​​a sphere if its radius is 7 cm.

Decision:

Let’s use the first formula (via the radius):

S = 4 ⋅ 3,14 ⋅ (7 cm)² = 615,44 cm².

Task 2

The surface area of ​​a sphere is 200,96 cm². Find its diameter.

Decision:

We derive the diameter value from the corresponding formula for calculating the area: