Question

A circular flower bed is surrounded by a path 4m wide. The diameter of the flower bed is a circular flower bed is surrounded by a path 4 m wide. The diameter of the flower bed is 66m what is the area of this path?​

Answer 1

Answer:

Diameter of the circular flower bed=66m

∴ Radius of circular flower bed(r)=266=33m

∴ Radius of circular flower bed with 4 m wide path(R)=33+4=37m

According to the question,

Area of path=Area of bigger circle−Area of smaller circle

=πR2−πr2=π(R2−r2)

=π[(37)2−(33)2]

=3.14[(37+33)(37−33)] [∵a2−b2=(a+b)(a−b)]

=3.14×70×4

=879.20m2.

Therefore, the area of the path is 879.20m2.

I hope this will helps you☺✌

please mark as branist..

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

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

$\star$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).

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

$\star{\small{\underline{\boxed{\sf{Radius \: = \dfrac{Diameter}{2}}}}}} \\ \star{\small{\underline{\boxed{\sf{Area \: of \: circle \: = \pi radius ^ {2}}}}}}\\\star{\small{\underline{\boxed{\sf{Area \: of \: path \: = Area \: of \: flower \: bed \: and \: path \: together \: - Area \: of \: flower \: bed}}}}}$

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

~ 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 :

${\sf{:\implies Radius \: of \: flower\: bed \: and \: path \: together ...}} \\ \\ {\sf{:\implies 33+4}} \\ \\ {\sf{:\implies 37 \: m}} \\ \\ {\underline{\frak{37 \: m \: is \: radius \: flower \: bed \dots \dots}}}$

~ 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:

${\small{\underline{\boxed{\sf{Area \: of \: path \: = Area \: of \: flower \: bed \: and \: path \: together \: - Area \: of \: flower \: bed}}}}} \\ \\ {\sf{:\implies Area \: of \: path \: = Area \: of \: flower \: bed \: and \: path \: together \: - Area \: of \: flower \: bed}} \\ \\ {\sf{:\implies Area \: of \: path \: = 4298.66 - 3419.46}} \\ \\{\sf{:\implies Area \: of \: path \: = 879.20 \: metres^{2}}} \\ \\{\underline{\frak{Area \: of \: the \: path \: = 879.20 \: metres^{2}}}}$