Sphere: Definition, Properties, Surface Area, Volume, Spheroid, and Hemisphere

Sphere is like circle in two-dimensional shape. But it is three-dimensional shape. Sphere things in daily life are like bubbles, marbles, balloons, balls, water drops, etc.

Definition of Sphere

Sphere is three-dimensional shape. It is a set of points that has same distance to the center. The distance is called radius (r). besides that, it has diameter (d) as twice of radius.

In other word diameter is a distance between a point in sphere to the opposite trough the center.

Sphere has not vertices and edge because it just has one surface (not flat area). Therefore, some of people called sphere as a ball shape.

Definition of Sphere

Properties of Sphere

There are properties of sphere:

  • It has not vertex and the edge
  • It is not a polyhedron
  • All of points in sphere has same distance to the center
  • It is perfectly symmetrical
  • It has curved face not flat face

Surface Area of Sphere

Surface of sphere is just one face but it is not flat surface. Surface area of sphere is

Surface Area of Sphere

Surface area = 4 x p x r2

Volume of Sphere

Volume of sphere means capacity in the sphere.

Volume of Sphere

Volume of sphere = 4/3 x p x r3

Spheroid

Spheroid base on an ellipse. it is also called as ellipsoid. It is the difference between a sphere that base on a circle and the spheroid. Because of it base on an ellipse it has two different radii (semi minor and semimajor axis). Besides that, it is also flat on the radius.

Spheroid

Hemisphere

Hemisphere is a half of sphere. In another words, if a sphere is cut into two symmetrical pieces trough the center then it is called hemisphere. Because of it is half of sphere then the volume and surface area are half of volume and surface area of a sphere.

Hemisphere

Examples

1. Determine surface area of a sphere if it has diameter 7 cm.

Answer

Diameter = 7 cm

Then radius = 7/2 = 3.5 cm

Surface area = 4 x p x r2

= 4 x (22/7) x (3.5)2

= 154 cm2

2. Determine surface area and volume of a sphere if it has radius 5 cm.

Answer
  • Surface area = 4 x p x r2

= 4 x 3.14 x 52

= 314 cm2

  • Volume = 4/3 x p x r3

= 4/3 x 3.14 x 53

= 523.33 cm3

3. Determine a half of volume of hemisphere if the diameter is 14cm.

Answer

Diameter = 14 cm then radius = 7 cm

Hemisphere is half of sphere, then

Volume = 4/3 x p x r3

= (1/2) {(1/2) x 4/3 x 22/7 x 73}

= (1/2) {(1/2) x 1437.333}

= (1/2) (718.666)

= 359.333 cm3

Note: it can be said that it asked ¼ of sphere.

4. There are two spheres. Small sphere has radius 6 cm and the larger is 9 cm. Small sphere is inside of the larger ones. Determine the volume between both of them.

Answer

Volume between both of them = volume larger sphere – volume small sphere

  • Volume small sphere = 4/3 x p x r3 

= 4/3 x p x 63

= 288p

  • Volume larger sphere = 4/3 x p x r3 

= 4/3 x p x 93 

= 972p

  • Volume between of them = 972p – 288p = 684p