Book: RS Aggarwal - Mathematics

Chapter: 18. Area of Circle, Sector and Segment

Subject: Maths - Class 10th

Q. No. 3 of Exercise 18A

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3
What is the diameter of a circle whose area is equal to the sum of the areas of two circles of diameter 10 cm and 24 cm?

Given:

Let the two circles be C1 and C2 with diameters 10 cm and 24 cm respectively.

Area of circle, C = Area of C1 + Area of C2 …… (i)

Radius of C1, r1 = = 5 cm

and Radius of C2, r2 = = 12 cm

Area of circle = πr2 …… (ii)

Area of C1 = πr12

=

=

= cm2

Similarly, Area of C2 = πr22

=

= 22/7 × 144

= cm2

Using equation (i), we have

Area of C = +

= cm2

Now, using equation (ii), we have

× r2 =

r2 =

r2 = 169

r =

r = 13 cm

Diameter = 2 × r

= 2 × 13

= 26 cm

Hence, the diameter of the circle is 26 cm.

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