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

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

Answer 2

Answer:

Diameter =84 m, Radius =42 m

Outer radius =42+3.5 m =45.5 m

Outer area from center = πR

2

=3.14×(45.5)

2

=6500.58m

2

Inner area = πr

2

=3.14×42×42

=5538.96m

2

Area of round = (6500.58−5538.96)m

2

=961.62m

2

Cost of construction = Rs. 2.40perm

2

∴ cost of construction = Rs. 2.40×961.62

=Rs.2307.88.