Question

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

Answer 1

$\maltese \ {\pmb{\underline{\sf{ Required \ Solution ... }}}}$

• A circular flower bed is surrounded by a path 4m wide.
• Diameter of Flowering Bed is 66m

$\maltese \ {\pmb{\underline{\sf{ Conditions ... }}}}$

The Diameter of circular Flower bed Excluding Path is 66m but if we can add length of Path in Length of bed then adding both side of Path into bed.

The Diamter of the Whole circular Bed including Path will be 74m.

$\maltese \ {\pmb{\underline{\sf{ Formular \ Concept ... }}}}$

$\circ \ {\underline{\boxed{\sf\large{ Area_{(Path)} = πR^2 - πr^2 }}}}$

Here,

• R = Radius of the Whole circle Including Path
• r = Radius of the Flower bed Excluding Path

$\maltese \ {\pmb{\underline{\sf{ Final \ Solution ... }}}}$

Now, We can Substitute values that we've discussed and derived above as that :-

$\colon\implies{\sf{ Area_{(Path)} = Area_{(Circle \ including \ Path)} - Area_{(Circle \ Excluding \ Path)} }} \\ \\ \\ \colon\implies{\sf{ πR^2-πr^2 }} \\ \\ \\ \colon\implies{\sf{ π(R^2-r^2) }} \\ \\ \\ \colon\implies{\sf{ \dfrac{22}{7} [(37)^2-(33)^2)] }} \\ \\ \\ \colon\implies{\sf{ \dfrac{22}{7} [1369-1089] }} \\ \\ \\ \colon\implies{\sf{ \dfrac{22}{ \cancel{7} } [ \cancel{280} ] }} \\ \\ \\ \colon\implies{\sf{ 22 \times 40 }} \\ \\ \\ \colon\implies{\underline{\boxed{\sf\purple{ 880 \ m^2 _{(Path)} }}}}$

Hence,

${\pmb{\underline{\sf{ The \ Area \ of \ the \ Path \ is \ 880 \ m^2. }}}} \bigstar$

Answer 2

$\underline{\underline{\maltese\: \: \textbf{\textsf{Question}}}}$

• A cicular flower bed is surrounded by a path 4m wide. the diameter of the flower bed is 66m.What is the area of the path?

$\underline{\underline{\maltese\: \: \textbf{\textsf{Answer}}}}$

• The required area of the path is 879.20 sq.m

$\underline{\underline{\maltese\: \: \textbf{\textsf{Given \: }}}}$

• Circular flower bed is surrounded by a path 4m wide
• Diameter of the flower bed is 66m

$\underline{\underline{\maltese\: \: \textbf{\textsf{To \: Find}}}}$

• The area of path

$\underline{\underline{\maltese\: \: \textbf{\textsf{Solution}}}}$

• As we have asked to find the area of path where path is 4m and diameter of the circle is 66m

• But we don't know about radius of the both circle

• Firstly, we may find its radius of both circle.

• As per as given question we may find area of path by its reqiured formula.

Finding radius :-

• Big circle radius = 4+33= 37
• small circle = 66÷2=33

${ \underline{ \underline{ \fbox{ \sf{Area \: of \: path \: = Area \: of \: bigcircle - Area \: of \: small \: circle}}}}}$

$\mapsto \sf \: \pi { \gamma }^{2} - \pi { \gamma }^{2}$

$\mapsto \sf \: \pi( {37}^{2} - {33}^{2} )$

$\mapsto \sf3.14( {37}^{2} - {33}^{2} )$

As using algebric expression formula,

$\longmapsto \sf \: {a}^{2} - {b}^{2}$

$\mapsto \sf \: (a + b) \times (a - b)$

$\mapsto \sf \: (70) \times (4)$

$\mapsto \sf \:\pi \times 70 \times 4$

$\mapsto \sf 3.14 \times 70 \times 4$

$\mapsto \sf \frac{3 1 4}{ \cancel1 \cancel0 \cancel0} \times 7 \cancel0 \times \cancel4 \: 2$

$\mapsto \sf\frac{314 \times 7 \times 2}{5}$

$\mapsto \: \frac{4306}{5}$

${\longmapsto\tt{Area \: of \: path = 879.20 {m}^{2} }}$