Question

the sum of the radii of two circles is 35 cm and the difference of their areas is 770cm.find their circumferences. ​

Answer 1

Answer:

Circumference of circle (1) = 132 cm

Circumference of circle (2) = 88 cm

Step-by-step explanation:

Let $r_1\:and\:r_2$ be the radii of the given twio circles respectively.

Given:

$r_1+r_2=35$

$\pi{r_1}^2-\pi{r_2}^2=770$

$\pi[{r_1}^2-{r_2}^2]=770$

$\frac{22}{7}({r_1}-{r_2})({r_1}+{r_2})=770$

$22({r_1}-{r_2})(5)=770$

$110({r_1}-{r_2})=770$

${r_1}-{r_2}=7$

Now, we have

$r_1+r_2=35$...............(1)

$r_1-r_2=7$...............(2)

Adding (1) and (2)

$2r_1=42$

$r_1=21$

(1)⇒

$21+r_2=35$

$r_2=35-21$

$r_2=14$

Circumference of circle (1)

$=2\pi{r_1}$

$=2*\frac{22}{7}*21$

$=2*22*3$

$=132$ cm

Circumference of circle (2)

$=2\pi{r_2}$

$=2*\frac{22}{7}*14$

$=2*22*2$

$=88$ cm