The area enclosed by the circumferences of two concentric circles is $346.5 c m^{2}$ . If the circumference of the inner circle is $88$ cm, then the radius of the outer circle is

88

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17.5

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35

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9.3

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Solution

The correct option is D $17.5$ cm
$G i v e n - O i s t h e c e n t r e o f t w o c o n c e n t r i c c i r c l e s w i t h o u t e r$

$r a d i u s O A = r_{2} & i n n e r c i c u m f e r e n c e = C = 88 c m .$

$a r . r i n g b e t w e e n t h e c i r c l e s = 346.5 {c m}^{2} .$

$T o f i n d o u t -$

$r_{2} = ?$

$S o l u t i o n -$

$i n n e r c i c u m f e r e n c e = 88 c m .$

$L e t t h e r a d i u s o f t h e i n n e r c i r c l e b e r_{1} .$

$∴ r_{1} = \frac{C}{2 π} = \frac{346.5}{2 \times \frac{22}{7}} c m = 14 c m .$

$S o a r . r i n g = a r . o u t e r c i r c l e - a r . i n n e r c i r c l e = π {{r_{2}}^{2} - {r_{1}}^{2}}$

$⟹ 346.5 = \frac{22}{7} \times {{r_{2}}^{2} - {r_{1}}^{2}}$

${⟹ r}_{2}^{2} = 306.25$

$⟹ r_{2} = 17.5 c m .$

$∴ T h e r a d i u s o f t h e o u t e r c i r c l e = 17.5 c m .$

$A n s - O p t i o n B .$

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The area enclosed by the circumferences of two concentric circles is 346.5cm2. If the circumference of the inner circle is 88 cm, then the radius of the outer circle is

The area enclosed by the circumferences of two concentric circles is $346.5 c m^{2}$ . If the circumference of the inner circle is $88$ cm, then the radius of the outer circle is