Question

a circular Park of 20 metre diameter has a circular path of width 1 m just inside the boundary find the area of path in the centre of the park there is a square platform of 2 m side find the area of the path excluding the platform ​

Answer 1

Answer:

According to question, area of circular path

Area =

\pi\left(R^{2}-r^{2}\right)

Where R = Outer area and r = Inner area

\pi\left(10^{2}-9^{2}\right)=19 \pi m^{2}

Answer 2

Answer:

(1) Area of circular path = 59.66m² (can be rounded to 59.7m² if needed)

(2) Area of the park excluding the platform = 310m²

Step-by-step explanation:

Finding the area of the entire circular park:

Diameter of the park = 20m

radius = 20/2 = 10m

Area of the circular park = πr²

=> 3.14 × (10)² = 3.14 × (10×10) = 3.14 × 100 = 314m²

(1) Finding the area of the path:

so if a platform right inside of the boundary has a width of 1m, then the

diameter of the park will reduce by 1m from both sides as the path runs all around the park and the diameter is a imaginary straight line running right through the centre of the park..just imagine it..

so the total diameter of the entire park = 20m, so excluding the circular path, the new diameter will now be:

20m - (1m+1m , 1m from each side) = 20m-2m = 18m

so using the same area formula but different radius,

new diameter = 18m

new radius = 18/2 = 9m

Area of the park excluding the circular path = πr²

=> 3.14 × (9)² = 3.14 × (9×9) = 3.14 × 81 = 254.34m²

now, Area of path = Area of entire park - Area of park excluding the circular path:

=> 314m² - 254.34m² = 59.66m²(Answer)

(2) Finding the Area of the path excluding the square platform:

let's first find the area of the square -

Area of square = Side × Side

=> 2m × 2m = 4m²

Area of the park excluding the platform = Area of the entire circular park - Area of the Square platform

=> 314m² - 4m² = 310m²(Answer)

     

Thanks, hope you benefitted from this.