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

Explanation:

Here, radius of a circular garden = 84 ÷ 2 = 42 m

Area of the circular garden = begin mathsize 16px style straight pi end styler2 = 22/7 × 42 × 42 = 5544 m2

Width of the road = 3.5 m

radius = 42 + 3.5 = 45.5 m

Total area = begin mathsize 16px style straight pi end styler2 = 22/7 × 45.5 × 45.5 = 6506.5 m2

Area of the road = 6506.5 - 5544 = 962.5 m2

The cost of constructing the road at Rs.20 per square meter = 962.5 × 20 =Rs. 19250

Answer 2

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