Question

a circular bed is surrounded by a path is 4m wide. the diameter of the flower bed is 66 m. what is the area of this path.​

Answer 1

area of the path = area of the circular bed with the path - area of the circular bed

879.2m^2

Answer 2

Answer:

The area of the path is 810 m².

Step-by-step-explanation:

In figure,

Bigger circle shows the circular bed and path.

Samller circle shows flower bed.

Diameter of smaller circle ( d ) = 66 m

∴ Radius of smaller circle ( r ) = d / 2 = 66 / 2 = 33 m

Path length = 4 m

Now,

Radius of bigger circle ( R ) = Radius of smaller circle + Path length

⇒ R = r + 4

⇒ R = 33 + 4

⇒ R = 37 m

Now,

The area of bigger circle is sum of areas of smaller circle and path. So, the area of path can be calculated by subtracting area of smaller circle from area of bigger circle.

∴ Area of path length = Area of bigger circle - Area of smaller circle

⇒ Area of path length = π R² - π r²

⇒ Area of path length = π ( R² - r² )

We know that,

a² - b² = ( a + b ) ( a - b )

⇒ Area of path = π ( R + r ) ( R - r )

⇒ Area of path = π ( 37 + 33 ) ( 37 - 33 )

⇒ Area of path = π * 70 * 4

⇒ Area of path = ( 22 / 7 ) * 70 * 4

⇒ Area of path = 22 * 70 ÷ 7 * 4

⇒ Area of path = 88 * 10

⇒ Area of path = 810 m²

∴ The area of the path is 810 m².