Q. 24.4( 221 Votes )

The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.

Answer :

Radius (r1) of 1st circle = 8 cm

Radius (r2) of 2nd circle = 6 cm


Let the radius of 3rd circle be r


Area of 1stcircle = r12 = π (8)2 = 64π


Area of 2nd circle = πr22 = π (6)2 = 36 π


Given that,


Area of 3rd circle = Area of 1st circle + Area of 2nd circle


πr2 = πr12 + πr22


πr2 = 64 π + 36 π


πr2 = 100 π


r2 = 100


r =


But we know that the radius cannot be negative. Hence, the radius of the circle having area equal to the sum of the areas of the two circles is 10 cm


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Area Related with Circles47 mins
Quiz | Imp. Qs. on Circles37 mins
Quiz | Testing Your Knowledge on Circles32 mins
Short Cut Trick to Find Area of Triangle43 mins
Champ Quiz | Area Related with the Circle45 mins
Tricks to MemoriseFREE Class
Smart and Effective study is the Key of success45 mins
How To Give Dynamic Input to JAVA program?63 mins
Various Tricks for How to Study Effectively32 mins
Ways to Study Smart30 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses