Question

The circumference of two concentric circles are 704 m and 660 m, respectively. Find
the difference in their radii.​

Answer 1

$\fbox{\texttt{\green{Answer:}}}$

Difference in the radii of the two concentric circles = 7 m

$\fbox{\texttt{\pink{Given:}}}$

Circumference of larger circle ($\bold{C_1}$)= 704 m

Circumference of smaller circle ($\bold{C_2}$)= 660 m

$\fbox{\texttt{\orange{To\:find:}}}$

Difference in the radii of the two circles.

$\fbox{\texttt{\red{How\:to\:Find:}}}$

We know, the formula for finding the circumference of a circle = $\bold{2\pi\:r}$

Applying the above formula for ($\bold{C_1}$), we get,

$\implies\bold{2\pi\:r_1=704}$

$\implies\bold{r_1=\dfrac{704}{2}\times{}\dfrac{7}{22}}$

$\implies\bold{r_1=16\times{}7=112\:m}$

Applying the formula for ($\bold{C_2}$), we get,

$\implies\bold{2\pi\:r_2=660}$

$\implies\bold{r_2=\dfrac{660}{2}\times{}\dfrac{7}{22}}$

$\implies\bold{r_2=15\times{}7=105\:m}$

$\rule{200}3$

$\therefore$ Difference in the radii of the two concentric circles would be,

$\implies\bold{r_1-r_2=112-105}$

$\implies\bold{7\:m}$

Answer 2

Answer:

circumference of a circle = \bold{2\pi\:r}2πr

Applying the above formula for (\bold{C_1}C

1

), we get,

\implies\bold{2\pi\:r_1=704}⟹2πr

1

=704

\implies\bold{r_1=\dfrac{704}{2}\times{}\dfrac{7}{22}}⟹r

1

=

2

704

×

22

7

\implies\bold{r_1=16\times{}7=112\:m}⟹r

1

=16×7=112m

Applying the formula for (\bold{C_2}C

2

), we get,

\implies\bold{2\pi\:r_2=660}⟹2πr

2

=660

\implies\bold{r_2=\dfrac{660}{2}\times{}\dfrac{7}{22}}⟹r

2

=

2

660

×

22

7

\implies\bold{r_2=15\times{}7=105\:m}⟹r

2

=15×7=105m

\rule{200}3

\therefore∴ Difference in the radii of the two concentric circles would be,

\implies\bold{r_1-r_2=112-105}⟹r

1

−r

2

=112−105

\implies\bold{7\:m}⟹7m