Question

find the area of ring between two concentric circles whose circumference are 75cm and 55cm​

Answer 1

Answer:

Step-by-step explanation:

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.

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

Circumference of 1st circle=2πr

88=2 x 22/7 x r

r=88 x 7/44

r=2 x 7

r=14cm

Circumference of 2nd circle = 2πR

132 = 2 X 22/7 X R

R=132 X 7/44

R = 21 cm

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

                         = π r*2-πR*2

                         = π(r*2-R*2)

                         = 22/7(21*2-14*2)

                         = 22/7 X 245

                         = 22 X 35

                         = 770 cm²

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

Answer 2

Answer:

• We have the circumference of two concentric circles 75cm and 55cm

$\bold{we \: know \: that \: circumference \: of \: a \: circle \: is \: given \: by = > \: 2\pi \: r}$

So, in 1 st case 2πr = 75 cm

$= > 2 \times \frac{22}{7} \times r = 75 \\ \\ = >r = \frac{75 \times7}{44} \\ \\ = > r = \frac{375}{44} \\ \\ = > r = 8.5cm$

Similarly, in 2 nd case 2πr= 55cm

$= > 2\pi \: r = 55 \\ \\ = >2 \times \frac{22}{7} \times r = 55 \\ \\ = > r = \frac{55 \times 7}{44} \\ \\ = >r = \frac{385}{44} \\ \\ = > r = 0.7cm$

So ,the area if the ring is equal to the subtraction of the area of two concentric circles✓

$\red{area \: of \: the \: ring \: is \: as \: follows \: }$

$= > \green{area \: of \: ring = } \bold{(\pi \times \: r1 ^{2}) - (\pi \times \: r2 ^{2}) }$

$= > \green{area \: of \: \:ring \: = } \bold({ \frac{22}{7} \times (8.5)^{2} \times} ) - ( \frac{22}{7} \times (0.7)^{2} )$

$= > \green{area \: of \: the \: ring} = \bold{ (\frac{22}{7} \times 72.25) -( \frac{22}{7} \times 0.49) }$

$= > \green{area \: of \: the \: ring = } \bold{ \frac{1509.5}{7} - \frac{10.78}{7} } \\ \\ = > \green{area \: of \: the \: ring = } \bold{215.6 - 1.5}$

$= > \boxed{\green{area \:of \:the \: ring = } \bold{ \red{214.1m ^{2} }}}$