Tuesday, March 5, 2013

28-Mensuration Problem 3

Blog-28

Dear Students,


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)

Please Click on the BLOG-30 (Simple Method to Solve Mensuration Problem (2)& BLOG-25 (Simple Method to Solve Mensuration Problem) to see more problems on Mensuration. (for the Students of 8th grade to 10th Grade)


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 Volume of as cone of height 5 cm is 753.6 cubic centimeters. Find the radius of the base of the cone. (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 [ ].

Given: 1) The volume of a cone = 753.6 Cubic Centimeter
          2) The height of a cone = 5 cm.
To find: The radius of the Base of a cone.

Solution:

1) We Know that the volume of a cone V = 1/3 π r2  h

  Therefore

                           3 v
                r= -------------                        ------------(1)
                                  π  h

                          3 x 753.6
2)              r= -------------------     
                                   3.14 x 5
                        [Multiply Numerator & denominator by 100]

                           3 x 75360
     so         r= -------------------     
                                    314 x 5

[Here we need to get Right Hand Side as the perfect Square, so try to get one more 3 from  75360 as one 3 is already available in the numerator simply by dividing 75360 by 3]


                          3 x 3 x 25120
3)               r= --------------------     
                                     314 x 5

[Here take the benefit of 5 available in the denominator. we can make it as 10 by multiplying numerator and denominator by 2]


                           3 x 3 x 2 x 25120
4)               r= -------------------------     
                                      314 x 2 x 5

                           3 x 3 x 2 x 25120
                   r= ------------------------   
                                          314 x 10

                           3 x 3 x 2 x 2512
                   r= -------------------------     
                                            314 

[Take 2 out from 2512 to get numerator in the form of perfect square]


                            3 x 3 x 2 x 2 x 1256
5)                r= -----------------------------     
                                              314 

[As 1256 is an even number, directly we can take 4 out from 1256]


                            3 x 3 x 2 x 2 x 4 x 314
6)                r= ---------------------------------     
                                                 314 

[dividing numerator and denominator by 314 we get]


7)                r=  3 x 3 x 2 x 2 x 4
                   
                   r=  (3 x 3 x 4 x 4)

So we have    r =  3 x 4

                    r = 12

So the radius of the base of a cone 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.


Anil Satpute