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

Algebra ->  Circles -> SOLUTION: The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36cm and 20 cm is (A) 56 cm (B) 42 cm (C) 28 cm (D) 16 cm       Log On


   

Question 238034: The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36cm and 20 cm is
(A) 56 cm (B) 42 cm (C) 28 cm (D) 16 cm
Answer by anantha(86) About Me  (Show Source):
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sol:
in this problem 3 circles are given
let the radius of the 1 st circle be r
circumference of 1st circle=2*pi*r
and diameter of the 2nd circle=36cm
circumference of 2nd circle=pi*diameter of 2nd circle=pi*36=36pi
diameter of the 3rd circle=20cm
circumference of the 3rd circle=pi*20=20pi
according to the problem
circumference of 1st circle=circumference of 2nd circle +circumference of 3rd circle
2*pi*r=36pi+20pi
2*pi*r=56pi
dividing both sides by pi
2*pi*r/pi=56pi/pi
2r=56
dividing both sides by 2
2r/2=56/2
r=28cm