# calculate the sphere examples

## sphere problem 1:

A sphere has a radius of 8 cm.
a) calculate the surface area
b) calculate the volume

A = 4 * r² * π

A = 4 * 8² * π

A = 804.25 cm².

A: The surface area is 804.25 cm².

V = 4 * r³ * π : 3

V = 4 * 8³ * π : 3    (π = 3.1415..)

V = 2 144.66 cm³

A: The volume is 2 144.66 cm³.

## sphere problem 2:

A sphere has a diameter of 12 cm.

a) calculate the surface area

b) calculate the volume

A = 4 * r² * π

A = 4 * 6² * π

A = 452.39 cm².

A: The surface area is 452.39 cm².

V = 4 * r³ * π : 3

V = 4 * 6³ * π : 3

V = 904.78 cm³

A: The volume is 904.78 cm³.

## sphere problem 3:

The surface area of a sphere is 76.8 cm².

b) calculate the volume

A = 4 * r² * π

76.8 = 4 * r² * π     / : 4

19,2 = r² * π     / : π

6,11..  = r²   / √

r = 2.47 cm.

A: The radius is 2.47 cm.

V = 4 * r³ * π : 3

V = 4 * 2.47³ * π : 3

V = 63.12 cm³

A: The volume is 63.12 cm³.

## sphere problem 4:

The volume of a sphere is 104 cm³.
b) calculate the surface area

V = 4 * r³ * π : 3

104 = 4 * r³ * π : 3    / * 3

312 = 4 * r³ * π     / : 4

78 = r³ * π     / : π

24,282….  = r³       / ³√

r = 2.92 cm.

A: The radius is 2.92 cm.