Book: RS Aggarwal - Mathematics
Chapter: 18. Area of Circle, Sector and Segment
Subject: Maths - Class 10th
Q. No. 12 of Exercise 18A
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12
The radii of two circles are 8 cm and 6 cm. Find the radius of the circle having area equal to the sum of the areas of the two circles.
Given:
Radius of one of the circles, C1 = 8 cm = r1
Radius of the other circle, C2 = 6 cm = r2
Let the other circle be C with radius ‘r’.
Area of C = Area of C1 + Area of C2 …… (i)
∵ Area of circle = πr2
∴ Area of C1 = πr12 = 
× 8 × 8 = 
and Area of C2 = πr22 = 
× 6 × 6 = 
Using (i), we have
πr2 = 
+ 
= 
× r2 = 
r2 = 
× 
= 100
r2 = 100
r = √100 = 10 or r = 10
Hence, the radius of the circle is 10 cm.
