Question

the sum of the radii of the two circles is 140cm and the difference of their circumferences is 88 cm.find the diameters of the circles.

Answer 1

This is the required solution.

Answer 2

Answer:

The diameter of first circle is 125.99 cm and Diameter of another circle is 154.01 cm

Step-by-step explanation:

Let the radius of one circle be x

Since we are given that the sum of the radii of the two circles is 140cm

So, the radius of another circle = 140-x

Formula of circumference =$2\pi r$

So, circumference of first circle = $2\pi x$

Circumference of another circle =  $2\pi (140-x)$

Since we are given that the difference of their circumferences is 88 cm

⇒ $88=2\pi (140-x)-2\pi x$

⇒ $88=2\pi (140-x-x)$

⇒ $88=2\pi (140-2x)$

⇒ $44=3.14 \times(140-2x)$

⇒ $\frac{44}{3.14}=(140-2x)$

⇒ $14.01=(140-2x)$

⇒ $2x=(140-14.01)$

⇒ $2x=125.99$

⇒ $x=\frac{125.99}{2}$

⇒ $x=62.995$

So, radius of first circle = 62.995 cm

Diameter = radius *2 = 62.995*2=125.99 cm

Another radius = 140-x=140-62.995=77.005 cm

Diameter of another circle = 77.005*2=154.01 cm

Hence the diameter of first circle is 125.99 cm and Diameter of another circle is 154.01 cm