Question

find the area of the ring between two concentric circles,whose circumference are 88 cm and 132 cm

Answer 1

Answer: The answer is 770 cm².

Step-by-step explanation: As given in the question and shown in the attached figure,  two concentric circles have circumferences 88 cm and 132 cm. Let 'r' and 'R' be the radius of smaller and bigger circle respectively. We are to find the area of the ring "D".

Now, if 'c' and 'C' be the the circumferences of the smaller circle and bigger circle, then we have

$c=2\pi r=88\\\\\Rightarrow \pi r=44\\\\\Rightarrow \dfrac{22}{7}r=44\\\\\Rightarrow r=14,$

and

$C=2\pi R=132\\\\\Rightarrow \pi R=66\\\\\Rightarrow \dfrac{22}{7}R=66\\\\\Rightarrow R=21.$

So, r = 14 cm  and  R = 21 cm.

Therefore, if 'a' and 'A' be the areas of the smaller and bigger circle respectively, then

$a=\pi r^2=196\pi~\textup{cm}^2$

and

$A=\pi R^2=441\pi~\textup{cm}^2.$

So, area of the ring "D" is

$A_D=A-a=441\pi-196\pi=245\pi=245\times \dfrac{22}{7}=770~\textup{cm}^2.$

Answer 2

Answer:

Area of Ring Between two concentric circles is 770 cm²

Step-by-step explanation:

Given: Circumference of two circle are 88 cm  and 132 cm

To Find: Area of ring between two concentric circles.

Circumference of circle = $2\pi r$

Using this formula first we calculate the radius of both circles.

Circumference of 1st circle = $2\pi r$

88 = $2\frac{22}{7}\times r$

88 = $2\frac{22}{7}\times r$

$r=88\times\frac{7}{44}$

$r=2\times7$

r = 14 cm

Circumference of 2nd circle = $2\pi R$

132 = $2\frac{22}{7}\times R$

132 = $2\frac{22}{7}\times R$

$R=132\times\frac{7}{44}$

$R=3\times7$

R = 21 cm

Area of the ring = Area of 2nd circle - Area of 1st circle

                          = $\pi R^2 - \pi r^2$

                          = $\pi\times(R^2-r^2)$

                          = $\frac{22}{7}\times(21^2-14^2)$

                          = $\frac{22}{7}\times(441-196)$

                          = $\frac{22}{7}\times245$

                          = $22\times35$

                          = 770 cm²

Therefore, Area of Ring Between two concentric circles is 770 cm²