Question

If the sum of the two radii of two circles is $7$ cm and the difference of their circumference is $8$ cm, the two circumferences will be

• A. $34$ cm and $26$ cm
• B. $30$ cm and $26$ cm
• C. $34$ cm and $20$ cm
• D. $35$ cm and $26$ cm

Answer 1

The correct option is C $34$ cm and $20$ cm

Let the two radii of two circles be $r_1$ and $r_2$ respectively
$\therefore r_1+r_2=7$ ...(i)
and $2\pi r_1-2\pi r_2=8$
$r_1-r_2=\frac{8}{2\pi }=\frac{8\times 7}{2\times 22}$
$r_1-r_2=\frac{14}{11}$ ...(ii)
On solving equation (i) and (ii)
$r_1=\frac{91}{22}$
$r_2=\frac{63}{22}$
$\therefore$ Circumference of the first circle
$=2\pi r_1=\frac{2\times 22}{7}\times \frac{91}{22}=26cm$
Circumference of the second circle
$=2\pi r_2=\frac{2\times 22}{7}\times \frac{63}{22}=18cm$