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The sum of the radii of two circles is 140 cm and the difference of their circumferences is 88 cm. Find the diameters of the circles.
Given:
The sum of the radii of two circles is 140 cm and the difference of their circumferences is 88 cm.
To do:
We have to find the diameters of the circles.
Solution:
Let the radius of the two circles be $r_1$ and $r_2$.
We know that,
Circumference of a circle of radius $r=2 \pi r$
Therefore,
The sum of the radii of two circles $=140\ cm$.
$r_1+r_2=140$..............(i)
The difference of the circumferences of two circles $=88\ cm$.
$2\pi r_1-2\pi r_2=88$
$2\times\frac{22}{7}(r_1-r_2)=88$
$r_1-r_2=2(7)$
$r_1-r_2=14$...........(ii)
Adding equations (i) and (ii), we get,
$r_1+r_2+r_1-r_2=140+14$
$2r_1=154$
$r_1=77\ cm$
$\Rightarrow r_2=140-77=63\ cm$
$\Rightarrow d_1=2r_1=2(77)=154\ cm$
$\Rightarrow d_2=2r_2=2(63)=126\ cm$
The diameters of the circles are $154\ cm$ and $126\ cm$.