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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

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28 cm

20 cm

14 cm

10 cm

answer is A.

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Detailed Solution

Given that, circumference of a circle is equal to the sum of the circumferences of the two circles of diameters

36 cm

and

20 cm

.
The diameter of the circle is twice the radius of the circle.
The circumference of the circle with diameter

36 cm

is,

C 1 = π (36)

And circumference of the circle with diameter

20 cm

is,

C 2 = π (20)

And circumference of circle with diameter

D

is,

C = π D

.
Equate the sum of circumference

C 1

and

C 2

with

C

to obtain the diameter of the circle,

C 1 + C 2 = C ⇒ 20 π + 36 π = π D ⇒ 56 π = π D ⇒ 56 = D

Simplify further for the radius,

⇒ 56 = 2 R ⇒ R = 562 ⇒ R = 28

Therefore, the radius of that circle is

28

cm.
Hence the correct option is 1.

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