Question

$\huge{\underline{\pmb{\frak{\pink{Question}}}}}$
⠀⠀
A circular flower bed is surrounded by a path 4 m wide. The diameter of the flower bed is 66 m. What is the area of this path?
( $\pi$ = 3.14).

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Answer 1

Given -

• Width of path is 4 m

• Diameter of flower bed is 66 m

To find -

• Area of the path

Formula used -

• Area of circle

Solution -

In the question, we are given with the width of path and the diameter of the flower bed, and we need to find the area of the path, for that we will first find the radius, after that we will find the area of the flower bed without path and then we will add the the width of path then we will find the area of flower bed including path, then we will subract both the area, that will give us area of path.

Let -

The area of flower bed without path, be termed as A¹.

Now -

→ Diameter = 66 m

→ Radius = 66/2 m

→ Radius, r = 33 m

Area of Circle -

πr²

On substituting the values -

→ A¹ = πr²

→ A¹ = 3.14 × (33)² m²

→ A¹ = 3.14 × 1089 m²

→ A¹ = 3419.46 m²

Now -

We will find the area of the flower bed including the path, for that we will add 4 m in the radius of the flower bed.

So -

→ Radius, r = 33 m

→ Radius, r = 33 + 4 m

→ Radius, r = 37 m

Now -

we will again the area of circle to find the area of flower bed including path.

→ A² = πr²

→ A² = 3.14 × (37)² m²

→ A² = 3.14 × 1369 m²

→ A² = 4298.66 m²

At the end -

We will subract the area of flower bed Including the path from the flower bed excluding the path.

→ A² - A¹

→ 4298.66 m² - 3419.46 m²

→ 879.20 m²

Therefore, the area of the path is 879.20m²

________________________________

Answer 2

${\large{\pmb{\sf{\underline{\maltese \: \: Understanding \; the \; Question...}}}}}$

★ This question says that a circular flower bed is surrounded by a path 4 metres in breadth. The diameter of that flower bed is 66 metres. We have to find out the area of that path. Also given that we have to take the value of π as 3.14 It is as given because the pi's (π) value is also given by ${\sf{\dfrac{22}{7}}}$

${\large{\pmb{\sf{\underline{\maltese \: \: Given \; that...}}}}}$

➼ A circular flower bed is given.

➼ Flower bed is surrounded by a path.

➼ Breadth of the path = 4 metres

➼ Diameter of flower bed = 66 metres

${\large{\pmb{\sf{\underline{\maltese \: \: To \; find...}}}}}$

➼ Area of the given path

${\large{\pmb{\sf{\underline{\maltese \: \: Solution...}}}}}$

➼ Area of the given path = 879.20 m²

${\large{\pmb{\sf{\underline{\maltese \: \: Using \; concepts...}}}}}$

➼ Formula to convert diameter into radius. Means formula to find radius.

➼ Formula to find area of circle.

➼ Formula to find area of path(according to the given question).

${\large{\pmb{\sf{\underline{\maltese \: \: Using \; formulas...}}}}}$

${\small{\underline{\boxed{\sf{Radius \: = \dfrac{Diameter}{2}}}}}}$

${\small{\underline{\boxed{\sf{Area \: of \: circle \: = \pi radius^{2}}}}}}$

${\small{\underline{\boxed{\sf{Area \: of \: path \: = Area \: of \: flower \: bed \: and \: path \: together \: - Area \: of \: flower \: bed}}}}}$

${\large{\pmb{\sf{\underline{\maltese \: \: Full \; Solution...}}}}}$

~ As it's already given that the diameter of the flower bed is 66 metres. So as we already knew that we have to use formula to find area of circle and it include radius not diameter so let us convert diameter into radius.

${\small{\underline{\boxed{\sf{Radius \: = \dfrac{Diameter}{2}}}}}}$

${\sf{:\implies Radius \: = \dfrac{Diameter}{2}}}$

${\sf{:\implies Radius \: = \dfrac{66}{2}}}$

${\sf{:\implies Radius \: = 33 \: metres}}$

${\underline{\frak{33 \: m\: is \: radius \: of \: flower \: bed}}}$

~ Now by using formula to find area of circle we have to find the area of the flower bed. We just have to put the values according to the formula. Let's do it!

${\small{\underline{\boxed{\sf{Area \: of \: circle \: = \pi radius^{2}}}}}}$

${\sf{:\implies Area \: of \: circle \: = \pi radius^{2}}}$

${\sf{:\implies Area \: of \: flower \: bed \: = \pi radius^{2}}}$

${\sf{:\implies Area \: of \: flower \: bed \: = 3.14 \times 33^{2}}}$

${\sf{:\implies Area \: of \: flower \: bed \: = 3.14 \times 33 \times 33}}$

${\sf{:\implies Area \: of \: flower \: bed \: = 3.14 \times 1089}}$

${\sf{:\implies Area \: of \: flower \: bed \: = 3419.46 \: metres^{2}}}$

${\underline{\frak{3419.46 \: m^{2} \: is \: the \: area \: of \: flower \: bed}}}$

~ Now as it's given that a circular flower bed is surrounded by a path 4 m wide. Henceforth, radius of flower bed and path together is given below :

${\sf{:\implies Radius \: of \: flower\: bed \: and \: path \: together \rightarrow}}$

${\sf{:\implies 33+4}}$

${\sf{:\implies 37 \: m}}$

${\underline{\frak{37 \: m \: is \: radius \: flower \: bed \dots \dots}}}$

~ Now by using formula to find area of circle again let us find the area of flower bed and path together, steps are given below :

${\small{\underline{\boxed{\sf{Area \: of \: circle \: = \pi radius^{2}}}}}}$

${\sf{:\implies Area \: of \: circle \: = \pi radius^{2}}}$

${\sf{:\implies Area \: of \: flower \: bed \dots \dots \: = \pi radius^{2}}}$

${\sf{:\implies Area \: of \: flower \: bed \dots \dots \: = 3.14 \times 37^{2}}}$

${\sf{:\implies Area \: of \: flower \: bed \dots \dots \: = 3.14 \times 37 \times 37}}$

${\sf{:\implies Area \: of \: flower \: bed \dots \dots \: = 3.14 \times 1369}}$

${\sf{:\implies Area \: of \: flower \: bed \dots \dots \: = 4298. 66 \: m}}$

${\underline{\frak{4298. 66 \: m \: is \: area \: of \: flower \: bed \dots \dots}}}$

~ Now at last let us find the area of the path by using the given formula:

${\small{\underline{\boxed{\sf{Area \: of \: path \: = Area \: of \: flower \: bed \: and \: path \: together \: - Area \: of \: flower \: bed}}}}}$

${\sf{:\implies Area \: of \: path \: = Area \: of \: flower \: bed \: and \: path \: together \: - Area \: of \: flower \: bed}}$

${\sf{:\implies Area \: of \: path \: = 4298.66 - 3419.46}}$

${\sf{:\implies Area \: of \: path \: = 879.20 \: metres^{2}}}$

${\underline{\frak{Area \: of \: the \: path \: = 879.20 \: metres^{2}}}}$