Question

find the diameter of circle whose circumference is equal to the sum of circumference of circle with radii 10 cm, 12 cm and 18 cm.

Answer 1

Circumference of the required circle
=
$2\pi10 + 2\pi12 + 2\pi18 \\ = 2\pi(10 + 12 + 18 )\\ = 2\pi40$
So
$2\pi \: r \: = 2\pi40 \\ so \\ r = 40$
Diameter = 2r
= 2*40 = 80cm

Answer 2

Let d be the required diameter, then radius of the circle d/2

It is given that,

2π d/2

=2π(10)+2π(12)+2π(18)

⇒2π(d/2)=2π(10+12+18)

⇒ d/2=40

⇒d=80cm.