On a rectangular plot, a horse is tied to a pole at a corner of a hut which measures 36 m by 12 m. The hut is at the centre of the rectangular grass patch and there is a 24 m wide border of grass patch around it. Given that the rope is 19 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 = 19 m
Length of the rope that covers the remaining area which is
14 of the small circle
= 19 - 12
= 7 m
Maximum area that the horse can feed on
= (
34 x π x 19 x 19) + (
14 x π x 7 x 7)
= 283π
= 888.62 m
2 (b)
Length of the rectangular plot
= 36 + (2 x 24)
= 36 + 48
= 84 m
Breadth of the rectangular plot
= 12 + (2 x 24)
= 12 + 48
= 60 m
Area of the rectangular plot
= 84 x 60
= 5040 m
2 Area of the hut
= 36 x 12
= 432 m
2 Area of the grass patch cannot be fed on
= 5040 - 432 - 888.62
= 3719.38 m
2 Answer(s): (a) 888.62 m
2; (b) 3719.38 m
2