On a rectangular plot, a horse is tied to a pole at a corner of a hut which measures 27 m by 9 m. The hut is at the centre of the rectangular grass patch and there is a 18 m wide border of grass patch around it. Given that the rope is 13 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 = 13 m
Length of the rope that covers the remaining area which is
14 of the small circle
= 13 - 9
= 4 m
Maximum area that the horse can feed on
= (
34 x π x 13 x 13) + (
14 x π x 4 x 4)
= 130.75π
= 410.555 m
2 (b)
Length of the rectangular plot
= 27 + (2 x 18)
= 27 + 36
= 63 m
Breadth of the rectangular plot
= 9 + (2 x 18)
= 9 + 36
= 45 m
Area of the rectangular plot
= 63 x 45
= 2835 m
2 Area of the hut
= 27 x 9
= 243 m
2 Area of the grass patch cannot be fed on
= 2835 - 243 - 410.555
= 2181.445 m
2 Answer(s): (a) 410.555 m
2; (b) 2181.445 m
2