Question

The circumference of two concentric rings are 88cm and 66cm respectively. Find the width between the rings.(Hint: find R and r)

Answer 1

Answer:

3.5 cm

Step-by-step explanation:

C1 = 2πR

88 = 2 * 22/7 * R

R = 88 * 7 / 2 * 22

R = 14 cm

C2 = 2πr

66 = 2 * 22/7 * r

r = 66 * 7 / 22 * 2

r = 21/2

r = 10.5 cm

Width = R - r

= 14 - 10.5

= 3.5 cm

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Answer 2

Question:

• The circumference of two concentric rings are 88cm and 66cm respectively. Find the width between the rings.(Hint: find R and r)

Given that:

• The circumference of two concentric rings are 88cm and 66cm respectively

Need to find :

• Find the width between the rings.

Solution :

Let R and r be the radius of the given cocentric circle.

Circumference of the outer circle of the ring :

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \displaystyle{ \purple{ \sf{ 2 {\pi}R = 88}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \displaystyle{ \sf{2 \times \frac{22}{7} \times R = 88}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \displaystyle{ \sf{R = \frac{88}{2 \times \frac{22}{7} } }}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \displaystyle{ \sf{R = \frac{88 \times 7} {2 \times 22}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \displaystyle{ \sf{R = \frac{ \cancel{88} \: \: ^{ \cancel{44} \: \: ^{22} } \times 7} { \cancel2 \times \cancel{22} \: \: ^{11} }}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \displaystyle{ \sf{R = \frac{\cancel{22} \: \: ^{2} \times 7} { \cancel{11}}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \displaystyle{ \boxed{ \sf{R = 14 \: cm}}} \red \bigstar$

Circumference of the inner circle of the ring :

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \displaystyle{ \green{ \sf{ 2 {\pi}r = 66}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \displaystyle{ \sf{2 \times \frac{22}{7} \times r = 66}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \displaystyle{ \sf{r = \frac{66}{2 \times \frac{22}{7} } }}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \displaystyle{ \sf{r = \frac{66 \times 7} {2 \times 22}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \displaystyle{ \sf{r = \frac{ \cancel{66} \: \: ^{ \cancel{33} \: \: ^{3} } \times 7} { 2 \times \cancel{22} \: \: ^{ \cancel{11}} }}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \displaystyle{ \sf{r = \frac{21}{2}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \displaystyle{ \boxed{ \sf{r = 10.5}}} \red \bigstar$

So,

The width of ring = R - r

The width of ring = 14 - 10.5

The width of ring = 3.5 cm

Henceforth, the width of ring is 3.5 cm $\red \bigstar$

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