Question

12. The areas of two concentric circles are 1386 cm’ and 1886.5 cm’ respectively. Find the width of the ring​

Answer 1

Question :-

• The areas of two concentric circles are 1386 cm’ and 1886.5 cm’ respectively. Find the width of the ring

Answer :-

• The width of the ring = 10.7

Given :-

• Areas of two concentric circles are 1386 cm’ and 1886.5 cm’

To find :-

• Find the width of the ring = ?

Solution :-

Let the radius of the outer circle be R

and radius of the inner circle be r

Area of the outer circle ,

$\\ \large \implies \bf \pi {R}^{2} = 1886.5$

$\\ \large \implies \bf {R}^{2} =\frac{1886.5 \times 7}{22}$

$\\ \large \implies \bf {R}^{2} =600.25$

$\\ \large \implies \bf R = 24.5 \: cm$

Area of inner circle ,

$\large \implies \bf \pi {r}^{2} = 600.25$

$\\ \large \implies \bf {r}^{2} = \frac{600.25 \times 7}{22}$

$\\ \large \implies \bf {r}^{2} = 190.10$

$\\ \large \implies \bf r = 13.8$

Width of the ring ,

R - r = 24.5 - 13.8 = 10.7cm

Answer 2

$\huge { \underline{\bf{ \red{Given-}}}}$

• Area of two concentric circles are 1386 cm² and 1886.5 cm².

$\huge { \underline{\bf{ \red{To \: find-}}}}$

• The width of the ring.

$\huge { \underline{\bf{ \red{Solution-}}}}$

Let the radius of the bigger circle be R and the smaller circle be r.

$\bf{Area \: of \: the \: outer\: circle = πR²} \\ \\ \bf \implies{1886.5\: {cm}^{2} = \frac{22}{7} \: {R}^{2} } \\ \\ \bf \implies{ \frac{1886.5 \times 7}{22} = {R}^{2} } \\ \\ \bf \implies{ 600.25 = {R}^{2} } \\ \\ \bf \implies{R = \sqrt{600.25} } \\ \\ \boxed{\bf \implies \gray{R = 24.5 \: cm}}$

$\bf {Area \: of \: inner \: circle = πr²} \\ \\ \bf \implies{1386 \: {cm}^{2} = 600.25 } \\ \\ \bf \implies{ \frac{1386 }{600.25} = {r}^{2} } \\ \\ \bf \implies {r}^{2} = 190.10 \\ \\ \bf \implies {r = \sqrt{190.10} } \\ \\ \boxed{ \bf \implies{ \gray{r = 13.8 \: cm}}}$

Therefore,

Width of the ring = Radius of outer circle - radius of inner circle.

$\bf \implies{24.5 \: cm - 13.8 \: cm} \\ \\ \boxed{\underline{\bf \implies{ \green{10.7cm}}}}$