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Q.

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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a

10 cm 

b

20 cm

c

14 cm

d

28 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=πD   .
Equate the sum of circumference C 1   and C 2   with C   to obtain the diameter of the circle,
C 1 + C 2 =C ⇒20π+36π =πD ⇒56π =πD ⇒56 =D    Simplify further for the radius,
⇒56 =2R ⇒R = 56 2 ⇒R =28  
Therefore, the radius of that circle is 28 cm.
Hence the correct option is 1.
 
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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