Question

The radii of the circles are 16cm and 20 cm. Find the radius of the circle whose circumference is equal to the sum of the circumferences of the two circles.​

Answer 1

Given:-

★ The radii of the circles are 16cm and 20 cm.

To Find :-

★ The radius of the circle whose circumference is equal to the sum of the circumferences of the two circles.

Solution :-

Given that,

The radii of the circles are 16cm and 20 cm.

Let radii of first circle be r (1) and 2nd circle be r (2).

Therefore,

r (1) = 16 cm

r (2) =20 cm

We know,

$\boxed{\tt{\bf{ Perimeter \ of \ the \ circle = 2 \pi r }}}$

Now, let's find the radius( R) of the circle whose circumference is equal to the sum of the circumferences of the two circles.

According to the question :-

2πR = 2πr(1) + 2πr(2)

⟹ R = 16 +20

⟹ R = 36 cm

Hence,

the radius( R) of the circle whose circumference is equal to the sum of the circumferences of the two circles is = 36 cm

Answer 2

Answer:

36cm

Explanation:

Let the two circles whose radii's are 16cm and 20cm be A and B, respectively. Let the circle whose circumference is to be found be C.

Circumference of circle A = 2πr(A)

Circumference of circle B = 2πr(B)  

Circumference of circle C = 2πr(C) = 2πr(A)+2πr(B)

this implies, 2πr(C) = 2π{r(A)+r(B)}

Thus, r(C) = r (A)+r(B) = 16+20 = 36cm

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