On a rectangular plot, a horse is tied to a pole at a corner of a hut which measures 45 m by 15 m. The hut is at the centre of the rectangular grass patch and there is a 30 m wide border of grass patch around it. Given that the rope is 25 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 = 25 m
Length of the rope that covers the remaining area which is
14 of the small circle
= 25 - 15
= 10 m
Maximum area that the horse can feed on
= (
34 x π x 25 x 25) + (
14 x π x 10 x 10)
= 493.75π
= 1550.375 m
2 (b)
Length of the rectangular plot
= 45 + (2 x 30)
= 45 + 60
= 105 m
Breadth of the rectangular plot
= 15 + (2 x 30)
= 15 + 60
= 75 m
Area of the rectangular plot
= 105 x 75
= 7875 m
2 Area of the hut
= 45 x 15
= 675 m
2 Area of the grass patch cannot be fed on
= 7875 - 675 - 1550.375
= 5649.625 m
2 Answer(s): (a) 1550.375 m
2; (b) 5649.625 m
2