It is a problem for Students 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 “By distributing our knowledge, it will boost & by keeping it only with us, it will reduce”).
I hope, you will definitely implement this technique to save you valuable time on Examinations or tests. 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 your thinking level. Only using this technique for solving some problems and getting good scores will not serve my purpose. I want that the entire world needs to improve its thinking skills so that everyone can invent so many beautiful things in 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 the world that we can also build the world with powerful thinking levels as everyone is competent.
Anil Satpute
Please see the following Problem.
I found some easier methods for this problem. so I would like to share this method with you. I am sure, that you may also find some easier methods than this. so Please come forward to share your method also.
Two non-congruent circles touch each other externally. The sum of their areas is 298 π square centimeters and the distance between their centers is 20 cm. Find the radii of both circles.
Solution
1) Let the radii of the circles be r1 & r2
2) As the circles touch each other externally, r1 + r2 = 20 cm
So r2 = 20 - r1
3) Sum of areas of circles = 298 π
So π r12 + π r22 = 298 π
r12 + r22 = 298
r12 + r22 + 2 r1 r2 - 2 r1 r2 = 298
(r1 + r2)2- 2 r1 r2 = 298 put (r1 + r2) = 20
(20)2- 2 r1 r2 = 298
(20)2- 298 = 2 r1 r2
400- 298 = 2 r1 r2 Dividing Numerator &
Denominator by 2
200- 149 = r1 r2
51 = r1 r2
r1 r2 = 51 put the r2 = (20 - r1)
r1 (20 - r1) = 51
20 r1 - r12 = 51
r12 - 20 r1 + 51 = 0
r12 - 17 r1 - 3 r1 + 51 = 0
r1 (r1 – 17) – 3 (r1 – 17) = 0
(r1 – 17) (r1 – 3) = 0
So r1 = 17 or r1 = 3
4) So the radii of the circles are 17 cm & 3 cm.
Like this, you can apply the technique to make use of simple calculations.
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 your thinking level. Only using this technique for solving some problems and getting good scores will not serve my purpose. I want that the entire world needs to improve its thinking skills so that everyone can invent so many beautiful things in 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 the world that we can also build the world with powerful thinking levels as everyone is competent.
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