On a rectangular plot, a horse is tied to a pole at a corner of a hut which measures 9 m by 3 m. The hut is at the centre of the rectangular grass patch and there is a 6 m wide border of grass patch around it. Given that the rope is 4 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 = 4 m
Length of the rope that covers the remaining area which is
14 of the small circle
= 4 - 3
= 1 m
Maximum area that the horse can feed on
= (
34 x π x 4 x 4) + (
14 x π x 1 x 1)
= 12.25π
= 38.465 m
2 (b)
Length of the rectangular plot
= 9 + (2 x 6)
= 9 + 12
= 21 m
Breadth of the rectangular plot
= 3 + (2 x 6)
= 3 + 12
= 15 m
Area of the rectangular plot
= 21 x 15
= 315 m
2 Area of the hut
= 9 x 3
= 27 m
2 Area of the grass patch cannot be fed on
= 315 - 27 - 38.465
= 249.535 m
2 Answer(s): (a) 38.465 m
2; (b) 249.535 m
2