Wednesday, March 6, 2013

29-Mensuration Problem 4

Blog-29


Dear Students,


Please Click on the the following links to go for 10th standard / 10th grade Mensuration Problems:
1) BLOG-22 (Simple Method to Solve Mensuration ProblemPublished on 26/02/2013
2) BLOG-27 (Simple Method to Solve Mensuration Problem (2)) Published on 04/03/2013
3) BLOG-28 (Mensuration Problem 3Published on 05/03/2013


I delivered the lecture on Mathematical Fun.  It was delivered in Indian Language “Marathi”. If you understand Marathi, Please click here to see my Lecture on youTube.

Secondly to think more about the studies of Mathematics, you are requested to participate in Program of Studies for Students and Parents given in my previous Blog. (Blog-11)

Once again, it is a problem from Student of 10th Standard / 10th grade. I would like to share the method of solving the problem & its presentation with you. Please go through it & make the habit of applying the same technique to solve other problems & please share this technique with your friends & relatives. (Please note one thing that “By distributing our knowledge, it will boost & by keeping it only with us, it will reduce”).
   
The Problem is very simple. Please see the following Problem.

The Cylindrical vessel of radius 15 cm contains water up to the height as 20 cm. A spherical metallic ball is dropped in to the water & the water level in the vessel increases by 10.24 cm. Find the radius of the metallic ball. (π = 3.14) (Note: Don’t use calculator)

Now we will the Simple method of calculations. Please understand the concepts / steps given in box Brackets [ ].

Please see the diagram related to the problem.



Given: 
1) The water level in the cylindrical vessel is increased by 10.24 so height (h) = 10.24 cm
2) Radius of the cylindrical vessel  r1 = 15 cm
3) The height of water in the cylindrical vessel = 20 cm (This height is not required for our calculations. It is given only to merge the metallic ball completely in to the water)
To find: The radius of the Base of a cone.

Solution:

1) According to the problem, 
     Volume of the Spherical Metallic Ball = Volume of the water displaced 
                                                     4/3 π r23 =  π r1h
                                                      4/3  r23  =   r1h
                                                             r23  =   3 r1h / 4
                                                             r23  =   3 x 15 x 15 x 10.24 / 4
                                   [Multiply Numerator & denominator by 100]
                                                             r23  =   3 x 15 x 15 x 1024 / 4 x 100
[Taking 3 from first 15 and another 3 from second 15 as we want RHS as perfect Cube]
                                                             r23  =   3 x 3 x 5  x 3 x 5 x 1024 / 4 x 100
                                   [Re-arranging the terms]
                                                             r23  =   (3 x 3 x 3)  x 5 x 5 x 1024 / 4 x 100
[Taking 4 from 1024 as we have 5 x 5 = 25 and when we multiply 25 by 4 we get 100 which will get cancelled with 100 of the denominator]
                                                             r23  =   (3 x 3 x 3)  x 5 x 5 x  4 x 256 / 4 x 100
[Taking 100  from Numerator and denominator, we get]
                                                             r23  =   (3 x 3 x 3)  x 256 / 
[Dividing 256 by 4 from denominator, we get]
                                                             r23  =   (3 x 3 x 3)  x 64
                                                             r23  =   (3 x 3 x 3)  x (4 x 4 x 4)
                                                             r2    =   (3 x 4)
                                                             r2    =   (12)

Therefore the radius of the spherical metallic ball is 12 cm.

Like this you can apply the technique to make use of simple calculations.

I hope, you will definitely implement this technique to save you valuable time of Examination or test. The same logical thinking can be applied to improve your thinking level.

I simply don't want to tell you to go with this simple method of calculation. I want that slowly, you need to mold yourself and improve the thinking level. Only using this technique for solving some problem and getting good scores will not serve my purpose. I want that the entire world need to improve the thinking skills so that every one can invent so many beautiful things of the human life.

This is possible only with the help of students like you along with your parents.

Please come ahead and start this beautiful work for yourself and show to the world that we can also build the world with powerful thinking level as every one is competent.

I thank Mrs. Jyoti Anil Satpute & Master Abhishek Anil Satpute for creative drawing work.

I also thank Mr Aaswad Anil Satpute for solving the software issues. 

Anil Satpute