Question

A circular field of radius 34 m has a circular path of uniform width of 5 m along and inside its boundary .Find the cost of paving the path the rate rs.36/m2

Answer 1

ANSWER:-

Given:

A circular field of radius is 34m has a circular path of uniform width of 5m along and inside its boundary.

To find:

The cost of paving the path the rate Rs.36/m².

Explanation:

We have,

• Circular field of radius is r= 34m [Outer]

We know that formula of area of the circle: πr²

⇒ Outer area of the circular field= $\frac{22}{7} *34*34$

⇒ Outer area of the circular field= $\frac{25432}{7} \:m^{2}$

⇒ Outer area of the circular field= 3633.14m²

Therefore,

Circular path of uniform width of 5m.

So,

Inner radius of the circular field is [34 -5]m

Inner radius of the circular field is 29m.

&

⇒ Inner area of the circular field= $\frac{22}{7} *29*29$

⇒ Inner area of the circular field= $\frac{18502}{7} m^{2}$

⇒ Inner area of the circular field= 2643.14m²

Remaining area of the circular field= Outer area - Inner area

Remaining area of the circular field= 3633.14m² - 2643.14m²

Remaining area of the circular field= 990m²

Now,

⇒ The cost of paving the path rate 1m² is Rs.36

⇒ The cost of paving the path rate 990m² is Rs. [990× 36]

The cost of paving the path rate is Rs.35640.