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.

Table of Contents

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.

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 = 4 x p x r^²

Volume of Sphere

Volume of sphere means capacity in the sphere.

Volume of sphere = 4/3 x p x r^³

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.

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.

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

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