Question

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

Answer 1

Area of circle = Area of circle of diameter 10 cm + Area of circle of diameter 24 cm

or Area of circle = Area of circle of radius 5 cm + Area of circle of radius 12 cm

πr² = π(5)² + π(12)²

πr² = 25 π + 144π = 169π

r = 13 So, required diameter is 26 cm.

Answer 2

Answer:

Area of circle=Area of circle of diameter 10cm+Area of circle of diameter24cm

or Area of circle = Area of circle of radius 5cm+ Area of circle of radius 12cm

⇒ πr

2

= π(5)

2

+ π(12)

2

⇒ πr

2

= 25π+ 144π= 169π

⇒ r

2

= 169 ∴ r= 13

So, required diameter is 26cm.