## 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.

Curved surface area A  =  4πr2

Volume of sphere  =  (4/3)πr3

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 :

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

=  (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.

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