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.
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.
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.
Radius = 7.5 cm
Total surface area of the sphere A = 4πr2
= 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
a) the volume of a sphere of radius 2.37 m
b) the radius of a sphere that has volume 2500 cm3.
(a) Volume of sphere (V ) = (4/3)πr3
Radius (r) = 2.37 m
= 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.
Diameter (a) = 2 m and radius = 1 m
(a) Surface area of sphere = 4πr2
= 4π cm2
(b) Cost of painting = $13.50
Cost for 1 coat = 4π (13.50)
= 54 x 3.14
Cost for 3 coats = 3(169.56)
So, the required cost is $508.68.
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