Sphere Area: formula and exercises

THE sphere area corresponds to the measure of the surface of this spatial geometric figure. Remember that the sphere is a solid, three-dimensional symmetrical figure.

Formula: How to Calculate?

To calculate the spherical surface area, use the formula:

THE_and = 4.π.r²

Where:

THE_and: sphere area
π (Pi): value constant 3.14
r: lightning

Note: O sphere radius corresponds to the distance between the center of the figure and its edge.

Solved Exercises

Calculate the area of ​​the spherical surfaces:

The) 7 cm radius sphere

THE_and = 4.π.r²
THE_and = 4.π.7
THE_and = 4.π.49
THE_and = 196π cm²

B) 12 cm diameter sphere

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

THE_and = 4.π.r²
THE_and = 4.π.6²
THE_and = 4.π.36
THE_and = 144π cm²

ç) sphere of volume 288π cm³

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

V_and = 4.π.r³/3

288π cm³ = 4.π.r³/3 (cut the π on both sides)
288. 3 = 4.r³
864 = 4.r³
864/4 = r³
216 = r³
r = ³√216
r = 6 cm

Once the radius measure is discovered, let's calculate the spherical surface area:

THE_and = 4.π.r²
THE_and = 4.π.6²
THE_and = 4.π.36
THE_and = 144π cm²

Entrance Exam Exercises with Feedback

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

a) 21%.
b) 11%.
c) 31%.
d) 24%.
e) 30%.

See Answer

Alternative to: 21%

2. (UFRS) A sphere with a radius of 2 cm is immersed in a cylindrical cup with a radius of 4 cm, until it touches the bottom, so that the water in the cup exactly covers the sphere.
Before the sphere was placed in the cup, the water height was:

a) 27/8 cm
b) 19/6 cm
c) 18/5 cm
d) 10/3 cm
e) 7/2 cm

See Answer

Alternative d: 10/3 cm

3. (UFSM) The surface area of ​​a sphere and the total area of ​​a straight circular cone are equal. If the radius of the base of the cone measures 4 cm and the volume of the cone is 16π cm³ the radius of the sphere is given by:

a) √3 cm
b) 2 cm
c) 3 cm
d) 4 cm
e) 4 + √2 cm

See Answer

Alternative c: 3 cm

Read too:

• The Sphere in Spatial Geometry
• Sphere Volume
• Spatial Geometry
• Math Formulas