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

Answer :

›»› The area of road this road is 3542 m².

Step-by-step explanation :

Given :

• Radius of a circular garden = 84 m.
• Inside it there is a 7 metre wide road along its circumference.

To Find :

• Area of this road = ?

Formula required :

Formula to calculate the area of circle is given by,

→ Area of circle = πr².

Here,

• The value of π is 22/7.
• r is the Radius.

Units,

• The unit of area of circle is m².
• The unit of radius is m.

Solution :

First we will find the remaining radii.

→ Remaining radii = Radius of circular garden - Width of the road with along its circular garden

→ Remaining radii = 84 - 7

→ Remaining radii = 77.

Since circular garden is in the shape of circle.

We know that, if we are given with the radius of a circular garden then we have the required formula, that is,

→ Area of circle = πr².

By using the formula to calculate the area of circular garden and substituting the given values in the formula, we get :

→ Area of circle = 22/7 * (84)²

→ Area of circle = 22/7 * 7056

→ Area of circle = 22 * 1008

→ Area of circle = 22176.

The area of circular garden is 22176 m².

Since circular garden excluding the road is also in the shape of circle.

We know that, if we are given with the remaining radii then we have the required formula, that is,

→ Area of circle = πr².

By using the formula to calculate the area of circular garden excluding the road and substituting the given values in the formula, we get :

→ Area of circle = 22/7 * (77)²

→ Area of circle = 22/7 * 5929

→ Area of circle = 22 * 847

→ Area of circle = 18634.

The area of circular garden excluding the road is 18634 m².

Now,

→ Area of this road = Area of circular garden - area of circular garden excluding the road.

→ Area of this road = 22176 - 18634

→ Area of this road = 3542

Hence, the area of this road is 3542 m².

Answer 2

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