On a rectangular plot, a horse is tied to a pole at a corner of a hut which measures 30 m by 10 m. The hut is at the centre of the rectangular grass patch and there is a 20 m wide border of grass patch around it. Given that the rope is 17 m long,
- what is the maximum grass patch area that the horse can feed on?
- find the total area of the grass patch that the horse cannot feed on. (Take π = 3.14)
(a)
Length of the rope that covers
34 of the big circle = 17 m
Length of the rope that covers the remaining area which is
14 of the small circle
= 17 - 10
= 7 m
Maximum area that the horse can feed on
= (
34 x π x 17 x 17) + (
14 x π x 7 x 7)
= 229π
= 719.06 m
2 (b)
Length of the rectangular plot
= 30 + (2 x 20)
= 30 + 40
= 70 m
Breadth of the rectangular plot
= 10 + (2 x 20)
= 10 + 40
= 50 m
Area of the rectangular plot
= 70 x 50
= 3500 m
2 Area of the hut
= 30 x 10
= 300 m
2 Area of the grass patch cannot be fed on
= 3500 - 300 - 719.06
= 2480.94 m
2 Answer(s): (a) 719.06 m
2; (b) 2480.94 m
2