Question

a road 10 m wide surrounds a circular park whose perimeter is 352 m Find the area of the road​

Answer 1

Given :

• Breadth of the road surrounding the circular park = 10 m
• Perimeter of the circular park = 352 m

To find :

• Area of the road

Concept :

Firstly find the radius of the circular park. To find the radius of the circular park use the formula of circumference of circle. After getting its value calculate the area of the circular park. Add 10 m in the radius of the circular park, the resultant value will be the radius of the circular park including the road. To find the area of the road subtract the area of the circular park from the area of circular park including the road.

➳ Formula of Circumference of circle :-

$\large \overline{ \underline{ \boxed{ \pmb {\rm Circumference = 2 \pi r}}}}$

➳ Formula to calculate area of circle :-

$\large \overline{ \underline{ \boxed{ \pmb {\rm Area \: of \: circle = \pi r^{2} }}}}$

Solution :

Perimeter = Circumference

∵ Both are the length of the boundary of any two dimensional figure.

Circumference of the circular park = 352 m

Using formula,

★ Circumference = 2πr

Substituting the given values,

$\\ \twoheadrightarrow \qquad \sf 352 = 2 \times \dfrac{22}{7} \times r$

$\\ \twoheadrightarrow \qquad \sf 352 = \dfrac{44}{7} \times r$

$\\ \twoheadrightarrow \qquad \sf 352 \times \dfrac{7}{44} = r$

$\\ \twoheadrightarrow \qquad \sf \not352 \times \dfrac{7}{ \not44} = r$

$\\ \twoheadrightarrow \qquad \sf 176 \times \dfrac{7}{22} = r$

$\\ \twoheadrightarrow \qquad \sf \not176 \times \dfrac{7}{ \not22} = r$

$\\ \twoheadrightarrow \qquad \sf 88 \times \dfrac{7}{11} = r$

$\\ \twoheadrightarrow \qquad \sf \not88 \times \dfrac{7}{ \not11} = r$

$\\ \twoheadrightarrow \qquad \sf 8 \times 7 = r$

$\\ \twoheadrightarrow \qquad \sf 56 = r$

$\\ \tt \to \quad Radius ~of~ the ~circular ~ park = 56 ~m$

Area of the circular park :-

Using formula,

★ Area of circle = πr²

Substituting the given values,

$\\ \twoheadrightarrow \sf \qquad Area \: of \: circular \: park = \dfrac{22}{7} \times ( {56})^{2}$

$\\ \twoheadrightarrow \sf \qquad Area \: of \: circular \: park = \dfrac{22}{7} \times 56 \times 56$

$\\ \twoheadrightarrow \sf \qquad Area \: of \: circular \: park = \dfrac{22}{ \not7} \times 56 \times \not56$

$\\ \twoheadrightarrow \sf \qquad Area \: of \: circular \: park = 22 \times 56 \times 8$

$\\ \twoheadrightarrow \sf \qquad Area \: of \: circular \: park = 9856$

$\\ \to \tt \quad Area \: of \: circular \: park = 9856 \: {m}^{2}$

Radius of the circular park + Road = 56 + 10 = 66 m

Therefore,

• Radius of circular park + road = 66 mm

Area of the circular park + road :-

Using formula,

★ Area of circle = πr²

Substituting the given values,

$\\ \twoheadrightarrow \sf \quad Area \: of \: circular \: park + road = \dfrac{22}{7} \times ( {66})^{2}$

$\\ \twoheadrightarrow \sf \quad Area \: of \: circular \: park + road = \dfrac{22}{7} \times 66 \times 66$

$\\ \twoheadrightarrow \sf \quad Area \: of \: circular \: park + road = 13690.29$

$\\ \to \tt \quad Area \: of \: circular \: park + road = 13690.29 \: {m}^{2}$

AREA OF ROAD :-

Area of the road = Area of circular park + road - Area of circular park

→ Area of the road = 13690.29 - 9856

→ Area of the road = 3,834.29

Therefore,

$\bf \underline{ {\tiny \maltese} \: \: Area \: of \: the \: road = 3,834.29 \: m^2}$

Answer 2

Given :

• A road 10 m wide surrounds a circular park whose perimeter is 352 m

To find :

• Area of the road.

Solution :

• In the question radius is not given so Firstly we will find the Radius of the circle(Park) by the perimeter Formula. Then we will find the area of the circle. Area of Circle = Circumference

• Then It is also given that a Road 10cm wide is surrounded a circular park. Then we will Add 10 cm to the Raduis. To find the area of Park we will use Formula (outer raduis)² - (Inner Radius)².

✰ Perimeter = 352 cm ✰

Let's Find out..!

Circumference = 2πr

→ 352 = 2 × 22/7 × R

→ 352 = 88/7 × R

→ R = 88/7 × 352

→ R = 56cm

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✰ Inner radius = 56cm

✰ Outer radius = 56 + 10 = 66cm

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Area of park = π(Outer Radius)² - (Inner)²

→ 22/7 (66)² - (56)²

→ 22/7 (4356 - 3136)

→ 3834.29m²

∴ Area of park is 3834.29m².

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