On a rectangular plot, a horse is tied to a pole at a corner of a hut which measures 18 m by 6 m. The hut is at the centre of the rectangular grass patch and there is a 12 m wide border of grass patch around it. Given that the rope is 9 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 = 9 m
Length of the rope that covers the remaining area which is
14 of the small circle
= 9 - 6
= 3 m
Maximum area that the horse can feed on
= (
34 x π x 9 x 9) + (
14 x π x 3 x 3)
= 63π
= 197.82 m
2 (b)
Length of the rectangular plot
= 18 + (2 x 12)
= 18 + 24
= 42 m
Breadth of the rectangular plot
= 6 + (2 x 12)
= 6 + 24
= 30 m
Area of the rectangular plot
= 42 x 30
= 1260 m
2 Area of the hut
= 18 x 6
= 108 m
2 Area of the grass patch cannot be fed on
= 1260 - 108 - 197.82
= 954.18 m
2 Answer(s): (a) 197.82 m
2; (b) 954.18 m
2