 ## 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 × 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.

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