Book: RS Aggarwal - Mathematics
Chapter: 18. Area of Circle, Sector and Segment
Subject: Maths - Class 10th
Q. No. 7 of Exercise 18A
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7
Find the diameter of the circle whose area is equal to the sum of the areas of two circles having radii 4 cm and 3 cm.
Given:
Let the two circles with radii 4 cm and 3 cm be C1 and C2 respectively.
⇒ r1 = 4 cm and r2 = 3 cm
Area of circle, C = Area of C1 + Area of C2 …… (i)
∵ Area of circle = πr2 …… (ii)
∴ Area of C1 = πr12
= 
= 
× 16 = 
cm2
Similarly, Area of C2 = πr22
= 
× 3 × 3
= 
× 9 = 
cm2
So, using (i), we have
Area of C = 
+ 
= 
cm2
Now, using (ii), we have
πr2 = 
× r2 = 
r2 = 
× 
= 25
r = √25 = 5
r = 5 cm
∵ Diameter = 2 × radius
∴ Diameter = 2 × 5 = 10 cm
Hence, diameter of the circle with area equal to the sum of two circles of radii 4 cm and 3cm is 10 cm.
