On a rectangular plot, a horse is tied to a pole at a corner of a hut which measures 33 m by 11 m. The hut is at the centre of the rectangular grass patch and there is a 22 m wide border of grass patch around it. Given that the rope is 20 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 = 20 m
Length of the rope that covers the remaining area which is
14 of the small circle
= 20 - 11
= 9 m
Maximum area that the horse can feed on
= (
34 x π x 20 x 20) + (
14 x π x 9 x 9)
= 320.25π
= 1005.585 m
2 (b)
Length of the rectangular plot
= 33 + (2 x 22)
= 33 + 44
= 77 m
Breadth of the rectangular plot
= 11 + (2 x 22)
= 11 + 44
= 55 m
Area of the rectangular plot
= 77 x 55
= 4235 m
2 Area of the hut
= 33 x 11
= 363 m
2 Area of the grass patch cannot be fed on
= 4235 - 363 - 1005.585
= 2866.415 m
2 Answer(s): (a) 1005.585 m
2; (b) 2866.415 m
2