Thursday, March 7, 2013

Mensuration Problem 5

Blog-33



Dear Students,

Please Click on the the following links to go for 10th standard / 10th grade Mensuration Problems:
1) BLOG-25 (Simple Method to Solve Mensuration ProblemPublished on 26/02/2013
2) BLOG-30 (Simple Method to Solve Mensuration Problem (2)) Published on 04/03/2013
3) BLOG-31 (Mensuration Problem 3Published on 05/03/2013
4) BLOG-32 (Mensuration Problem 4Published on 06/03/2013

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-14)

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”).
   
Please see the following Problem.

The radius and height of a Cylinder are in the ratio 4 : 9 and its volume is 19386.36 cubic centimeter. Find its radius. (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 ratio between radius and height is r : h = 4 : 9. ( so, h = 9 r / 4 )
2) The volume of the cylinder  V  = 19386.36 cubic centimeter.
To Find: The radius of the cylinder.

Solution

1) We know that the volume of the cylinder V =  π rh
    so                                                                 V = π r( 9 r / 4 )
    so                                                                 V = 9 π r  / 4 
    so                                                                 r3 = 4 V / 9 π 
    so                                                                 r3 = 4 x 19386.36 / 9 x 3.14 
         [Multiply Numerator & denominator by 100]
2) so                                                                 r3 = 4 x 1938636 / 9 x 314 
         [Here 1938636 is divisible by 9 divide Numerator & denominator by  9 we get]
3)  so                                                                 r3 = 4 x 215404 / 314 
         [Taking 2 out from 215404 as it is required for getting cube term to RHS along with existing 4]
4)  so                                                                 r3 = 4 x 2 x 107702 / 314
         [Here 107702 is divisible by 2 divide Numerator & denominator by  2 we get]
5)  so                                                                 r3 = 4 x 2 x 53851 / 157
         [Here 53851 is not divisible by 2, 3, 4, 5, 6, we will see for 7, (NOTE: we will see the test of divisibility of 7 in due course) so take 7 out from 53851]
6)  so                                                                 r3 = 4 x 2 x 7 x 7693 / 157
         [For getting perfect cube, we need to take 2 more 7's from 7693 one after another]
    so                                                                 r3 = 4 x 2 x 7 x 7 x 1099 / 157
7)  so                                                                 r3 = 4 x 2 x 7 x 7 x 7 x 157 / 157
         [Now an answer is in your hand. Simply devide Neumerator & denominator by 157 we get]
8)  so                                                                 r3 = 4 x 2 x 7 x 7 x 7
     so                                                                 r3 = (2 x 2 x 2) x (7 x 7 x 7)
     so                                                                 r = (2 x 7)
     so                                                                 r = (14)

Therefore the radius of the cylinder is 14 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