Question

Question 9
The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is
(A) 56 cm
(B) 42 cm
(C) 28 cm
(D) 16 cm

Answer 1

Circumference of first circle
$=2\pi r=\pi d_1=36\pi cm[given{d}_1=36cm]$

And circumference of second circle
$=\pi d_2=20\pi cm[given{d}_2=20cm]$

According to the given condition,

Circumference of circle
= Circumference of first circle + circumference of second circle]

$\Rightarrow \pi D=36\pi +20\pi$ [ where D is a diameter of a circle]

$\Rightarrow D=56cm$

So, diameter of a circle is 56 cm.

$\therefore$ Required radius of circle $=\frac{56}{2}=28cm$