Question

A circular park is surrounded by a road 21 m wide. if the radius of the park is 105 m, find the area of the road​

Answer 1

$\sf{\large{\underline{\underline{Question:}}}}$



A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, then find the area of the road.



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$\sf{\large{\underline{\underline{Answer}}}}$



15246 cm²



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$\huge \pink{ \mid \underline{ \overline{ \sf Brainly \: Solution :}} \mid}$



▶ Given,


Radius of Circular Park=105 m

Width of Road Around the Park=21 m

$\sf \therefore Radius \: of \: big \: circle = 105 + 21 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sf 126 \: m$
$\sf Area \: of \: road = Area \: of \: bigger \: circle - Area \: of \:circular \: park \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = \pi {R}^{2} - \pi {r}^{2} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = \pi \bigg(R {}^{2} - {r}^{2} \bigg) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = \pi \bigg[ {(126)}^{2} - {(105)}^{2} \bigg] \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = \frac{22}{7} \times (126 + 105)(126 - 105) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bigg[ \because a {}^{2} - b {}^{2} = (a + b)(a - b) \bigg] \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = \frac{22}{ \cancel7} \times 231 \times \cancel{21} \: ^ { \large3} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = 66 \times 231 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = 15246 \: cm {}^{2}$

$\huge \orange{ \boxed{ \boxed{ \sf{ \therefore Area \: of \: Road = 15246 \: {cm}^{2} }}}}$


✔✔ Hence, it is solved ✅✅.


$\huge \green{ \boxed{ \boxed{ \mathscr{THANKS}}}}$

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