SPHERE

Definition of Sphere :

This is a solid generated when a semicircle is being rotated about its diameter. In three dimensional space, this is also known as perfect round geometrical object.

A plane is at the center of the spherical solid divides the solid in to two equal parts. Each shape is called hemisphere.

Example :

A very good example we can say for spherical shaped solid is globe. Ball is another good example for spherical shaped solid.

Example 1 :

The formula for calculating the total surface area A of a sphere of radius r is A  =  4πr². 

Find:

a) the total surface area of a sphere of radius 7.5 cm

b) the radius, in cm, of a spherical balloon which has a surface area of 2 m².

Solution :

Radius  =  7.5 cm

Total surface area of the sphere  A  =  4πr²

=  4π(7.5)²

=  225π cm²

So, the total surface area of the sphere is 225π cm².

Example 2 :

A sphere of radius r has volume given by 

V  =  (4/3)πr³

Find :

a) the volume of a sphere of radius 2.37 m

b) the radius of a sphere that has volume 2500 cm³.

Solution : 

(a)  Volume of sphere (V ) =  (4/3)πr³

Radius (r)  =  2.37 m

=  (4/3)π(2.37)³

=  (4/3)π(133.12)

=  177.49 π cm³

(b)  Volume of sphere  =  2500 cm³

(4/3)πr³  =  2500

r³  =  2500/4.18

r  =  8.42 

Example 3 :

A spherical art piece has diameter 2 meters. Find 

(a)  The surface area of the sphere 

(b)  The cost of painting the sphere (with 3 coats) given each square meter will cost $13.50 for paint and labour.

Solution :

Diameter (a)  =  2 m and radius  =  1 m

(a)  Surface area of sphere  =  4πr²

=  4π(1)²

=  4π cm²

(b)  Cost of painting  =  $13.50

Cost for 1 coat  =  4π (13.50)

=  54π

=  54 x 3.14

=  169.56

Cost for 3 coats  =  3(169.56)

=  $508.68

So, the required cost is $508.68.

Related Pages

• How to find volume of sphere
• Volume of sphere practice problems 
• Surface area and volume of spheres
• Curved surface area and total surface area of sphere and hemisphere
• Examples on volume of sphere and hemisphere
• Volume of sphere and hemisphere worksheet

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