Question

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Answer 1

Question :

A circular park of Diameter 28 m has a circular path of width 3.5 m along the boundary of the park. Find the area of the path.

Given :

• Diameter = 28 m

• Width of the park = 3.5 m

Solution :

According to the Question , the path is built along the circular park.

If we carefully look at the diagram , we get to know that that the Circle with the path is also making a new circle.

So by the given information , we can find the radius of the new circle.

Radius of the new circle = Radius of the Circle + width of the park.

$\boxed{\begin{minipage}{7 cm} \bf{Radius\:of\:new\:Circle = \dfrac{28}{2} + 3.5} \\ \bigg[\because Radius = \dfrac{Diameter}{2}\bigg] \\ \\ \bf{Radius\:of\:new\:Circle = 14 + 3.5} \\ \\ \bf{Radius\:of\:new\:Circle = 17.5\:m} \end{minipage}}$

Hence, the radius of the new circle is 17.5 m

Now , the area of new circle and the area of the orginal Circle will give us the area of the path.

Area of orginal Circle :-

We know the formula for area of a Circle i.e,

$\underline{:\implies \bf{A = \pi r^{2}}}$

Using the above formula and substituting the values in it , we get :

$:\implies \bf{A = \dfrac{22}{7} \times 14^{2}}$

$:\implies \bf{A = \dfrac{22}{7} \times 14^{2}}$

$:\implies \bf{A = \dfrac{22}{7} \times 196}$

$:\implies \bf{A = 22 \times 28}$

$:\implies \bf{A = 616}$

$\underline{\therefore \bf{Area\:(A) = 616\:m^{2}}}$

Hence, the Area of the orginal Circle is 616 m².

Area of new Circle :-

We know the formula for area of a Circle i.e,

$\underline{:\implies \bf{A = \pi r^{2}}}$

Using the above formula and substituting the values in it , we get :

$:\implies \bf{A = \dfrac{22}{7} \times 17.5^{2}}$

$:\implies \bf{A = \dfrac{22}{7} \times 306.25}$

$:\implies \bf{A = 22 \times 43.75}$

$:\implies \bf{A = 962.5}$

$\underline{\therefore \bf{Area\:(A) = 962.5\:m^{2}}}$

Hence, the Area of the new Circle is 962.5 m².

Area of the path :-

==> Area of new Circle - area orginal Circle

==> (962.5 - 616) m²

==> 346.5 m²

Hence, the area of the path is 346.5 m².

Answer 2

Question :

A circular park of Diameter 28 m has a circular path of width 3.5 m along the boundary of the park. Find the area of the path.

Given :

Diameter = 28 m

Width of the park = 3.5 m

Solution :

According to the Question , the path is built along the circular park.

If we carefully look at the diagram , we get to know that that the Circle with the path is also making a new circle.

So by the given information , we can find the radius of the new circle.

Radius of the new circle = Radius of the Circle + width of the park.

Hence, the radius of the new circle is 17.5 m

Now , the area of new circle and the area of the orginal Circle will give us the area of the path.

Area of orginal Circle :-

We know the formula for area of a Circle i.e,

Using the above formula and substituting the values in it , we get :

Hence, the Area of the orginal Circle is 616 m².

Area of new Circle :-

We know the formula for area of a Circle i.e,

Using the above formula and substituting the values in it , we get :

Hence, the Area of the new Circle is 962.5 m².

Area of the path :-

==> Area of new Circle - area orginal Circle

==> (962.5 - 616) m²

==> 346.5 m²

Hence, the area of the path is 346.5 m².