Question

if radius of two concentric circle are 28cm and 18cm respectively if the perimeter and the area of the circles are numerically equal then find the radius of the circle​

Answer 1

Given :-

• Radius of first circle = $\sf{r_1=28 \:cm.}$

• Radius of second circle = $\sf{r_2=18 \:cm.}$

To Find :-

• Radius of the circle.

Solution :-

Let the radius of the required circle be r cm.

Circumference of small circle :-

$:\implies\:\rm{2\pi r_1}$

$:\implies\:\rm{2\pi \times 28}$

$:\implies\:\rm{56\:\pi }$

Circumference of larger circle :-

$:\implies\:\rm{2\pi r_2}$

$:\implies\:\rm{2\pi \times 18}$

$:\implies\:\rm{36\:\pi }$

Now,

According to the question :-

Circumference of the required circle = Sum of circumference of two circles.

$:\implies\:\rm{2\pi r=56\:\pi +36\:\pi }$

$:\implies\:\rm{2\pi r=92\:\pi }$

$:\implies\:\rm{ r=\dfrac{92\:\pi }{2\:\pi } }$

$:\implies\:\rm{ r=46 }$

Hence, the radius of required circle = r= 46 cm.