Question

A circular flower bed is 20m in diameter and has a circular sidewalk around it that is 2m wide. Find the area of the sidewalk in square meters.

Answer 1

Answer :

138.16m²

Explanation :

Circular flower bed with diameter = 20m.

And a side walk of 2m around it.

Find the area of sidewalk.

Following the figure,

→ Area of the sidewalk = Area of $\sf C_2$ - Area of $\sf C_1$

Let's calculate the area of $\sf C_1$ :

We know that,

Area of a circle = πr²

Where,

• r(radius) will be = 20/2 = 10m i.e., ½ of the diameter.
• Taking ‘π’ as 3.14

→ 3.14 × (10)²

→ 3.14 × 100

→ 314m²

And also, Calculating the area of $\sf C_2$

Where,

• radius will be 10 + 2 = 12m
• Taking 'π' as 3.14

∴ Area :

→ πr²

→ 3.14 × (12)²

→ 3.14 × 144

→ 452.16m²

Now,

Area of the sidewalk : $\sf C_2$ - $\sf C_1$

→ 452.16 - 314

→ 138.16m²

Required answer : 138.16m²

Answer 2

QuestioN :

A circular flower bed is 20m in diameter and has a circular sidewalk around it that is 2m wide. Find the area of the sidewalk in square meters.

GiveN :

• Circular flower bed = 20 m
• circular sidewalk = 2m wide

To FiNd :

• The area of the sidewalk in square meters.

ANswer :

The area of the sidewalk in square meters is 138.16 m².

SolutioN :

$\sf Radius\: of\: the \:flower \:bed\:=\: \dfrac{20}{2}$

$\sf \implies 10m$

$\sf Area \:of\: the\: flower\: bed\:=\:\pi r^2$

$\sf \implies 3.14\times10\times10$

$\sf \implies 314m^2$

If the path is all around the flower bed and it's width is 2m, then the radius of the flower bed along with the path will be = 10 + 2

$\sf \implies 12m$

$\therefore \sf it's \:\:area\:=\:\pi r^2$

$\sf \implies 3.14\times 12\times12$

$\sf \implies452.16\:m^2$

$\sf The\: area\: of\: the\: path\:=\:452.16-314$

$\sf \implies 138.16\:m^2$

∴Hence, The area of the sidewalk in square meters is 138.16m².

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