Question

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

Answer 1

To Find :-

• Difference in the radii of the two circles.

Solution :-

Given that,

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

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

We know

• Circumference of a circle = $\sf{2\pi\:r}$

Substituting the given values :-

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

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

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

$:\implies{\underline{\boxed{\frak{\red{ r_1= 112\; m}}}}}\;\bigstar$

⠀

Again,

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

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

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

$:\implies{\underline{\boxed{\frak{\red{ r_2= 105\; m}}}}}\;\bigstar$

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

$:\implies\sf{r_1-r_2=112-105}$

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

$:\implies{\underline{\boxed{\frak{\red{ r_1-r_2= 7\; m}}}}}\;\bigstar$

• Hence,difference in the radii of the two concentric circles = 7 m

________________________________

Answer 2

Step-by-step explanation:

To Find :-

Difference in the radii of the two circles.

Solution :-

Given that,

Circumference of larger circle (\bold{C_1}C

1

)= 704 m

Circumference of smaller circle (\bold{C_2}C

2

)= 660 m

We know

Circumference of a circle = \sf{2\pi\:r}2πr

Substituting the given values :-

:\implies\sf{2\pi\:r_1=704}:⟹2πr

1

=704

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

1

=

2

704

×

22

7

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

1

=16×7=112m

:\implies{\underline{\boxed{\frak{\red{ r_1= 112\; m}}}}}\;\bigstar:⟹

r

1

=112m

★

⠀

Again,

:\implies\sf{2\pi\:r_2=660}:⟹2πr

2

=660

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

2

=

2

660

×

22

7

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

2

=15×7=105m

:\implies{\underline{\boxed{\frak{\red{ r_2= 105\; m}}}}}\;\bigstar:⟹

r

2

=105m

★

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

:\implies\sf{r_1-r_2=112-105}:⟹r

1

−r

2

=112−105

:\implies\sf{7\:m}:⟹7m

:\implies{\underline{\boxed{\frak{\red{ r_1-r_2= 7\; m}}}}}\;\bigstar:⟹

r

1

−r

2

=7m

★

Hence,difference in the radii of the two concentric circles = 7 m

_______________________________