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 = 4πr^{2}
Volume of sphere = (4/3)πr^{3}
Example 1 :
The formula for calculating the total surface area A of a sphere of radius r is A = 4πr^{2}.
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 m^{2}.
Solution :
Radius = 7.5 cm
Total surface area of the sphere A = 4πr^{2}
= 4π(7.5)^{2}
= 225π cm^{2}
So, the total surface area of the sphere is 225π cm^{2}.
Example 2 :
A sphere of radius r has volume given by
V = (4/3)πr^{3}
Find :
a) the volume of a sphere of radius 2.37 m
b) the radius of a sphere that has volume 2500 cm^{3}.
Solution :
(a) Volume of sphere (V ) = (4/3)πr^{3}
Radius (r) = 2.37 m
= (4/3)π(2.37)^{3}
= (4/3)π(133.12)
= 177.49 π cm^{3}
(b) Volume of sphere = 2500 cm^{3}
(4/3)πr^{3 }= 2500
r^{3 }= 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 = 4πr^{2}
= 4π(1)^{2}
= 4π cm^{2}
(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.
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Aug 06, 22 11:56 PM
Aug 06, 22 11:31 PM
Aug 06, 22 09:01 AM