Question

The diameter of two circles are 38cm and 18cm.Find the diameter of the circle whose circumference is equal to sum of the circumferences of the two circles.​

Answer 1

Step-by-step explanation:

Diameter of circle 1 = 38 cm

Radius of circle 1 = \frac{38}{2}=19 cm

2

38

=19cm

Circumference of circle 1 = 2 \pi r = 2\pi (19)2πr=2π(19)

Diameter of circle 2 = 18 cm

Radius of circle 2 = \frac{18}{2}=9 cm

2

18

=9cm

Circumference of circle 2 = 2 \pi r = 2 \pi (9)2πr=2π(9)

SO, Circumference of two circle = 2\pi(19)+2 \pi (9)2π(19)+2π(9)

We are supposed to find the diameter of the circle whose circumference is equal to the circumference of two circles

So, Let the radius of that circle be R

So,\begin{gathered}2\pi R =2 \pi (19)+2 \pi (9)\\R=19+9\\R=28\end{gathered}

2πR=2π(19)+2π(9)

R=19+9

R=28

Diameter of circle = 28 \times 2 = 56 cm28×2=56cm

Hence the diameter of the circle whose circumference is equal to the circumference of two circles is 56 cm