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


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

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Solo Build It!

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. Law of Cosines Worksheet

    Aug 06, 22 11:56 PM

    Law of Cosines Worksheet

    Read More

  2. Laws of Cosines

    Aug 06, 22 11:31 PM

    Laws of Cosines - Proof - Solved Problems

    Read More

  3. Perpendiculars and Bisectors Worksheet

    Aug 06, 22 09:01 AM

    Perpendiculars and Bisectors Worksheet

    Read More