the diameter of a circular grass-field is 40m.
There is a road of width 1 m starting from 1 m
away of its end point. Calculate the
expenditure to grass the road at a rate of 26
paise per m^2.
Plz help with solution
I am puzzled by:
There is a road of width 1 m starting from 1 m
away of its end point.
I'll take a stab and say that the road is 1m away from the field. So its inner radius is 41 and its outer radius is 42.
So, the cost is rate * area =
π(42^2 - 41^2) * 26
Small codicil: The diameter is 40 m , not the radius
To calculate the expenditure to grass the road, we need to determine the area of the road and then multiply it by the given rate.
1. Find the radius of the circular grass-field:
The diameter is given as 40m, so the radius (r) is half of the diameter.
r = 40m / 2 = 20m
2. Find the total area of the circular grass-field:
The formula for the area of a circle is A = π * r^2, where π is a constant (approximately 3.14).
A = 3.14 * (20m)^2
A ≈ 3.14 * 400m^2
A ≈ 1256m^2
3. Find the area of the circular grass-field with the road:
The area of the circular grass-field with the road is equal to the total area of the larger circle minus the area of the smaller circle (field without the road).
The radius of the smaller circle is 20m (radius of the grass-field), and we need to add 1m on each side for the width of the road.
Area of the circular grass-field with the road = π * (21m)^2 - π * (20m)^2
Area of the circular grass-field with the road ≈ 3.14 * (441m^2) - 3.14 * (400m^2)
Area of the circular grass-field with the road ≈ 1381.4m^2 - 1256m^2
Area of the circular grass-field with the road ≈ 125.4m^2
4. Calculate the expenditure:
Expenditure = Area of the circular grass-field with the road * Rate
Expenditure = 125.4m^2 * 26 paise/m^2
Now, you can multiply the area (125.4m^2) by the rate (26 paise/m^2) to get the final expenditure.