On a rectangular plot, a horse is tied to a pole at a corner of a hut which measures 12 m by 4 m. The hut is at the centre of the rectangular grass patch and there is a 8 m wide border of grass patch around it. Given that the rope is 6 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 = 6 m
Length of the rope that covers the remaining area which is
14 of the small circle
= 6 - 4
= 2 m
Maximum area that the horse can feed on
= (
34 x π x 6 x 6) + (
14 x π x 2 x 2)
= 28π
= 87.92 m
2 (b)
Length of the rectangular plot
= 12 + (2 x 8)
= 12 + 16
= 28 m
Breadth of the rectangular plot
= 4 + (2 x 8)
= 4 + 16
= 20 m
Area of the rectangular plot
= 28 x 20
= 560 m
2 Area of the hut
= 12 x 4
= 48 m
2 Area of the grass patch cannot be fed on
= 560 - 48 - 87.92
= 424.08 m
2 Answer(s): (a) 87.92 m
2; (b) 424.08 m
2