Friday, March 15, 2013

Problem on Circle 2

 Blog-40

The BLOG on Simple Method of Multiplication will be published on 16/03/2013.

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 Problem) Published 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
  5) BLOG-33 (Mensuration Problem 5Published on 07/03/2013
  6) BLOG-34 (Trigonometry Problem 1Published on 08/03/2013
  7) BLOG-35 (Trigonometry Problem 2Published on 09/03/2013
  8) BLOG-36 (Trigonometry Problem 3Published on 11/03/2013
  9) BLOG-37 (Trigonometry Problem 4Published on 12/03/2013
10) BLOG-38 (Problem on Circle 1Published on 13/03/2013
11) BLOG-39 (Trigonometry Problem 5Published on 14/03/2013

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)

See the simple method of calculations for solving the Trigonometry Problem. There are so many methods to solve such type of problems. You also may have better solution for such type of problems, that can also shared with other students. Please see the following problem & it's solution which I find as easier one. If you have any other simple method, then please publish your method through this blog simply by writing the comments.


In the figure given bellow, PR = 6 units & PQ = 8 units. Semicircles are drawn taking
Sides PR, RQ & PQ as diameters. Find the area of the shaded portion RxPsQtPyR.
(π = 3.14).










Solution:

Given:  PR = 6 units, PQ 8 units
To Find: Area of the shaded Portion

1) In ∆ RPQ, Ð RPQ = 90°       [Angle inscribed in Semicircle is right angle]
2) In ∆ RPQ, RQ2 = PR2 + PQ2
                                 RQ2 = 62 + 82         
                                 RQ2 = 36 + 64
                                 RQ2 = 100
                                 RQ   = 10 Units.
3) Let radius of semicircle RxPm be r1, PsQn be r2 & RyPtQ be r3
4) Let Base & Height of ∆ RPQ   be PR = b = 6 & PQ = h = 8.
The above problem is solved by calculating for each values of radii, 3, 4 & 5 separately by multiplying each term by 3.14 & 1/2 in so many books. Here one should know tha
(32 + 42 – 52) = 0. So here you need not multiply all the three radii by 3.14 & 1/2. That's why I would like to tell you to think very properly & improve your application of thinking any where.  

Thinking in this direction will definitely improve your skills & the same can be utilized by you to apply every where.

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