(i) Longer path
l = 20 m; b = 2 m
The area of the Longer path = l x b
= 20 x 2 = 40 m²
shorter path, l = 15 m, b = 1 m
The area of the shorter path = I x b
= 15 x 1 = 15 m²
Area of middle portion = 2 m x 1m = 2 m²
Total area of the paths = 40 m² + 15 m² - 2m²
= 53 m²
(ii) The area of the rectangular field = L x B
= 20 x 15
= 300 m²
The area of the remaining portion = Area of field - Area of two paths
= 300 - 53 - 247m²
(iii) The cost of constructing the roads per sq .m = Rs 10
The total cost of constructing the roads for 55 sq.m = Rs 10 x 53
= Rs 530

The radius ofthe circle = 3 cm
Length of the rectangle= 8 x radius
= 8 x 3=24cm
Breath = 2 x radius
= 2 x 3=6 cm
Radius ofa circle r = 3cm
Area = πr²
The area of each circle = \(\cfrac { 22 }{ 7 } \times 3\times 3=\cfrac { 198 }{ 7 } =28.28^{ 2 }cm\) 

Area of pathway = Area of outer rectangle - Area of inner rectangle
= LB - lb
= 80 x 50 - 70 x 40
= 4000 - 2800 = 1200 m²

Radius of school ground (R) = 103 m
Width of a track = 3 m
Width of a tracks = 4 x 3 = 12 m
Inner radius of ground (r) = 103 - 12 = 91 m
Area of tracks \(=\pi\left(R^{2}-r^{2}\right) \text { sq. units } \)
\(=\frac{22}{7}(103 \times 103-91 \times 91) \)
\(=\frac{22}{7}(10609-8281) \)
\(=\frac{22}{7} \times 2328=7316.57 \mathrm{~m}^{2} \)
cost of construction of track of 1 sq.m = Rs. 50
cost of construction of track of 7316.57 sq. units = 50 x 7316.57
= Rs. 365828.50

Given length of rope = radius = 4.9 m
Area that the sheep can graze = \(\pi r^{2}\)
\(=\frac{22}{7} \times 4.9 \times 4.9\)
= 75.46 m²