The **area of the sphere** corresponds to the measurement of the surface of this spatial geometrical figure. Remember that the sphere is a solid and symmetrical three-dimensional figure.

## Formula: How to Calculate?

To calculate the spherical surface area, use the formula:

**A _{e} = 4. π .r ^{2}**

Where:

**A _{e}** : sphere area

**π**(Pi): constant value 3.14

**r**: radius

**Note** : the **radius of the sphere** corresponds to the distance between the center of the figure and its end.

## Solved Exercises

Calculate the area of spherical surfaces:

**a)** sphere of radius 7 cm

A _{e} = 4.π.r ^{2}

A _{e} = 4.π.7

A _{e} = 4.π.49**A _{e} = 196π cm ^{2}**

**b)** 12 cm diameter sphere

First of all, we must remember that the diameter is twice the radius measurement (d = 2r). Therefore, the radius of this sphere measures 6 cm.

A _{e} = 4.π.r ^{2}

A _{e} = 4.π.6 ^{2}

A _{e} = 4.π.36**A _{e} = 144π cm ^{2}**

**c)** sphere of volume 288π cm ^{3}

To perform this exercise we must remember the formula for the volume of the sphere:

**V _{and} = 4 **

**π**

**.r**

^{3}/3288 **π** cm ^{3} = 4 **π** .r ^{3} /3 (cuts the two sides of π)

288. 3 = 4.r ^{3}

864 = 4.r ^{3}

864/4 = r ^{3}

216 = r ^{3}

r = ^{3} √216**r = 6 cm**

Discovered the radius measure, let’s calculate the spherical surface area:

A _{e} = 4.π.r ^{2}

A _{e} = 4.π.6 ^{2}

A _{e} = 4.π.36**A _{e} = **

**144**

**π**

**cm**

^{2}## Vestibular Exercises with Feedback

**1** . (UNITAU) By increasing the radius of a sphere by 10%, its surface will increase:

a) 21%.

b) 11%.

c) 31%.

d) 24%.

e) 30%.

## Answer

Alternative to: 21%

**2** . (UFRS) A sphere of radius 2 cm is immersed in a cylindrical cup of 4 cm radius, until it touches the bottom, so that the water in the glass exactly covers the sphere.

Before the sphere was placed in the glass, the height of water was:

a) 27/8 cm

b) 19/6 cm

c

) 18/5 cm d) 10/3 cm

e) 7/2 cm

## Answer

Alternative d: 10/3 cm

**3** . (UFSM) The surface area of a sphere and the total area of a straight circular cone are the same. If the radius of the base of the cone measures 4 cm and the volume of the cone is 16π cm ^{3} the radius of the sphere is given by:

a) √3 cm

b) 2 cm

c) 3 cm

d) 4 cm

e) 4 + √2 cm

## Answer

Alternative c: 3 cm