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? (π = 3.14)

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Answer 1

$\huge\mathfrak{\underline{Correct\:question}}$

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? (π = 3.14)

_______________________________________

Given that:-

• A circular flower bed is surrounded by a path 4 m wide.

• The diameter of the flower bed is 66 m.

To find:-

• The area of the path

Answer:-

$\bold{STEP-BY-STEP-EXPLANATION}$

From the question it is given that,

Diameter of the flower bed = 66 m

Then,

Radius of the flower bed = d/2

= 66/2

= 33 m

Area of flower bed = πr2

= 3.14 × 332

= 3.14 × 1089

= 3419.46 m

Now we have to find area of the flower bed and path together

So, radius of flower bed and path together = 33 + 4 = 37 m

Area of the flower bed and path together = πr^2

= 3.14 × 372

= 3.14 × 1369

= 4298.66 m

Now,

Area of the path = Area of the flower bed and path together – Area of flower bed

= 4298.66 – 3419.46

= 879.20 m^2

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Answer 2

$\bf{\Huge{\underline{\boxed{\sf{\red{ANSWER\::}}}}}}$

$\bf{\Large{\underline{\bf{Given\::}}}}$

A circular flower bed is surrounded by a path 4m wide. The diameter of the flower bed is 66m.

$\bf{\Large{\underline{\bf{To\:find\::}}}}$

The area of this path.

$\bf{\Large{\underline{\boxed{\rm{\green{Explanation\::}}}}}}$

We have,

$\leadsto\rm{Diameter\:=\:66m}$

$\leadsto\rm{Radius\:=\:\frac{Diameter}{2} }$

$\leadsto\rm{Radius\:=\:\cancel{\frac{66}{2}}m }$

$\leadsto\rm{Radius\:(r)\:=\:33m}$

• $\bf{\Large{\boxed{\sf{\red{Area\:of\:smaller\:circle\::}}}}}}$

$\longmapsto\rm{Area\:=\:\pi r^{2} }$

$\longmapsto\rm{Area\:=\:[3.14*(33)^{2} ]m^{2} }$

$\longmapsto\rm{Area\:=\:(3.14*1089)m^{2} }$

$\longmapsto\rm{\orange{Area\:=\:3419.46m^{2} }}}$

• $\bf{\Large{\boxed{\sf{\red{Area\:of\:larger\:circle\::}}}}}}$

→ Larger radius of circle,(R) = radius + width of path

→ Larger radius of circle,(R) = (33 + 4)m

→ Larger radius of circle,(R) = 37m

Therefore,

$\longmapsto\rm{Area\:=\:\pi R^{2} }$

$\longmapsto\rm{Area\:=\:[3.14*(37)^{2} ]m^{2} }$

$\longmapsto\rm{Area\:=\:(3.14*1369)m^{2} }$

$\longmapsto\rm{\orange{Area\:=\:4298.66m^{2} }}}$

• $\bf{\Large{\boxed{\rm{\red{Area\:of\:the\:path\::}}}}}$

$\mapsto\sf{Area\:of\:larger\:circle\:(R)\:\:-\:\:Area\:of\:smaller\:circle\:(r)}$

$\mapsto\sf{4298.66m^{2} \:\:-\:\:3419.46m^{2} }$

$\mapsto\sf{\purple{879.2m^{2} }}$

Thus,

$\bf{\large{\boxed{\sf{\pink{The\:area\:of\:path\:=\:879.2m^{2} }}}}}$