Question

Find the diameter of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters $36$ m and $20$ m.

Answer 1

Given, two circles with diameters $36m$ & $20m$.

So, radius of first circle $=\frac{36}{2}m=18m$

Circumference$=2\pi r=2\pi \times 18m=36\pi m$

And, radius of second circle $=\frac{20}{2}m=10m$

Circumference$=2\pi r=2\pi \times 10m=20\pi m$

Sum of circumferences of two given circles $=(36\pi +20\pi )m=56\pi m$

Let $R$ be radius of the required circle

Circumference $=2\pi R$

ATQ,

$2\pi R=56\pi$

$\Rightarrow R=28$

So, diameter $D=2\times 28m=56m$

$\therefore$ Diameter of required circle is $56m$