Question

The ratio of the outer and inner circumference of a circular path as shown in the figure is 26 :25. If the path is 5 meter wide, then find
1) the area enclosed by the path
2) the diameter of the inner circle

Answer 1

Let the Inner radius be r .
And since the width of the path is 5m.
Therefore, the Outer radius is R = r + 5.
According to the question,
$\frac{inner \: circumference}{outer\: circumference} = \frac{26}{25} \\ = > \frac{2\pi(r + 5)}{2\pi r} = \frac{26}{25} \\ = > \frac{r + 5}{r} = \frac{26}{25} \\ = > 25(r + 5) = 26r \\ = > 25r + 125 = 26r \\ = > r = 125m$
Hence, Inner radius = 125m.
So, Outer Radius (R) = r + 5m = 125 + 5 = 130m.

1) The area of the path = The area of the outer circle - The area of the inner circle.
=> pi*(R^2) - pi*(r^2)
$\pi {(130)}^{2} - \pi {(125)}^{2} \\ = > \pi( {(130m)}^{2} - {(125m)}^{2} ) \\ = > \pi( 130m - 125m)(130m + 125m) \\ = > \pi \times 5m \times 255m \\ = > {1275m}^{2} \times 3.14 \\ = > {4003.5m}^{2}$
Therefore, Area of the path = 4003.5m^2

2)The diameter of the inner circle = 2r
= 2*125m = 250m

THERE YOU GO!!!.....

Answer 2

Answer:

Let the Inner radius be r .

And since the width of the path is 5m.

Therefore, the Outer radius is R = r + 5.

According to the question,

Hence, Inner radius = 125m.

So, Outer Radius (R) = r + 5m = 125 + 5 = 130m.

1) The area of the path = The area of the outer circle - The area of the inner circle.

=> pi*(R^2) - pi*(r^2)

Therefore, Area of the path = 4003.5m^2

2)The diameter of the inner circle = 2r

= 2*125m = 250m

Step-by-step explanation: