On a rectangular plot, a horse is tied to a pole at a corner of a hut which measures 30 m by 10 m. The hut is at the centre of the rectangular grass patch and there is a 20 m wide border of grass patch around it. Given that the rope is 15 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 = 15 m
Length of the rope that covers the remaining area which is
14 of the small circle
= 15 - 10
= 5 m
Maximum area that the horse can feed on
= (
34 x π x 15 x 15) + (
14 x π x 5 x 5)
= 175π
= 549.5 m
2 (b)
Length of the rectangular plot
= 30 + (2 x 20)
= 30 + 40
= 70 m
Breadth of the rectangular plot
= 10 + (2 x 20)
= 10 + 40
= 50 m
Area of the rectangular plot
= 70 x 50
= 3500 m
2 Area of the hut
= 30 x 10
= 300 m
2 Area of the grass patch cannot be fed on
= 3500 - 300 - 549.5
= 2650.5 m
2 Answer(s): (a) 549.5 m
2; (b) 2650.5 m
2