Question

The sum of the radii of two circles is 7 cm.and difference in circumference is 8 cm. Find the circumferences

Answer 1

hence the circumference are 26 cm and 18 cm .

Answer 2

Answer: The circumferences are 26 cm and 18 cm respectively.

Step-by-step explanation:

Since we have given that

Sum of radii of two circles = 7 cm

i.e. R+r=7 cm  ----------------------(1)

Difference in circumference = 8 cm

According to question, we get that

$2\pi (R-r)=8\\\\R-r=\dfrac{8}{2\pi}=\dfrac{4}{\pi}=\dfrac{28}{22}=\dfrac{14}{11}--------------(2)$

From Eq(1), and Eq(2), we get that

$R-r=\dfrac{14}{11}\\\\7-r-r=\dfrac{14}{11}\\\\7-2r=\dfrac{14}{11}\\\\-2r=\dfrac{14}{11}-7\\\\-2r=\dfrac{14-77}{11}\\\\-2r=\dfrac{-63}{11}\\\\r=\dfrac{63}{22}$

And the value of R is given by

$R=7-r\\\\R=7-\dfrac{63}{22}\\\\R=\dfrac{154-63}{22}\\\\R=\dfrac{91}{22}$

so, the circumferences would be

$2\pi R=2\times \dfrac{22}{7}\times \dfrac{91}{22}=26\ cm\\\\2\pi r=2\times \dfrac{22}{7}\times \dfrac{63}{22}=18\ cm$

Hence, the circumferences are 26 cm and 18 cm respectively.