Question

the radius of a circular garden is 84m. inside it there is a 7 metre wide road along its circumference. find the area of this road​

Answer 1

Solution :

Radius of circular garden : 84 m

Width of the road along the circumference of the garden : 7 m

Remaining radii : 77 m

To find : Area of Road

=> Total Area of circular garden - Area of circular garden excluding the road

=> π ( 84 )² - π ( 77)²

=> π × ( 161 ) × 7

=> 22/7 × 161 × 7

=> 22 × 161

=> 3542 m² .

Answer : The required area of this road is 3542 m² .

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Additional Information :

Area of a circle - π r²

Circumference of a circle : 2 π r

Area of a semi circle : ( 180/360 ) π r²

Circumference of semi circle : π r .

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Answer 2

$\begin{gathered} \huge \bf{ \pmb{ \color{black}{\underline{SOLUTION}}}} \\ \\ \bf { \pmb{ \gray{ \underline{ GIVEN }}}}\\ \small \cal Radius \: of \: Circular \: Garden = 84 \: m \\ \cal \small 7 \: m \: wide \: road \: along \: g arden \: Circumference \\ \\ \bf{ \pmb{ \gray{ \underline{TO \: \: FIND}}}} \\ \tt \: Area \: of \: the \: Road \\ \\ \bf{ \pmb{ \gray{ \underline{FORMULA \: \: USED}}}} \\ \rm \boxed{ \blue{ Area \: of \: Circle = πr²} }\\ \\ \bf{ \pmb{ \gray{ \overline{ \underline{ \mid \: CALCULATION \mid}} }}}\\ \sf \scriptsize{ Total \: Area \: of \: circular \: garden = \pi {(84)}^{2}} \\ \scriptsize{ \sf \: Area \: of \: circular \: garden \: excluding \: the \: road = \pi {(84 - 7)}^{2} = \pi {(77)}^{2}} \\ \red{ \sf \tiny{Area \: of \: Road = Total \: Area \: of \: circular \: garden - Area \: of \: circular \: garden \: excluding \: the \: road} }\\ \\ \bf \: π (84)² - π(77)² \\ \bf π[(84)²-(77)²] \\ \bf \: π[(84+77)(84-77)] \\ \bf \frac{22}{7} ×161×7 \\ \bf \: 3542 \\ \\ \large \bf { \pmb{ \gray{ \underline{ \ddag \: \: Final \: Answer \: \: \ddag}}}} \\ \boxed{\blue{ \tt{ \pmb {The \: required \: area \: of \: the \: road \: is \: 3542 \: m²}}}}\end{gathered}$