Question

A circular garden is surrounded internally by a 3m wide path. If the diameter of the
garden is 24 m, find the area of the path.
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Answer 1

Given:

Diameter of circular garden = 24m

Width of circular path = 3m

To find: The are of circular path = ?

Solution:

We know the relation between Radius, $r$ and Diameter, $d$ :

$r = \dfrac{d}{2}$

Please refer to the attached image.

So, radius of Circular Garden:

$R=\dfrac{24}{2} = 12\ m$

Circular path has a width of 3m, so Radius of inner circle:

$r = R - 3\\\Rightarrow r = 9\ m$

Area of circular path = Area of outer circle - Area of inner circle

We know that area of a circle is defined as:

Area $= \pi \times Radius^2$

So, area of circular path = $\pi R^{2} - \pi r^{2}$

$\Rightarrow \pi (12^2-9^2)\\\Rightarrow \dfrac{22}{7} \times 63\\\Rightarrow 22 \times 9\\\Rightarrow 198\ m^{2}$

So, area of circular path is = $198\ m^{2}$