On a rectangular plot, a horse is tied to a pole at a corner of a hut which measures 15 m by 5 m. The hut is at the centre of the rectangular grass patch and there is a 10 m wide border of grass patch around it. Given that the rope is 8 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 = 8 m
Length of the rope that covers the remaining area which is
14 of the small circle
= 8 - 5
= 3 m
Maximum area that the horse can feed on
= (
34 x π x 8 x 8) + (
14 x π x 3 x 3)
= 50.25π
= 157.785 m
2 (b)
Length of the rectangular plot
= 15 + (2 x 10)
= 15 + 20
= 35 m
Breadth of the rectangular plot
= 5 + (2 x 10)
= 5 + 20
= 25 m
Area of the rectangular plot
= 35 x 25
= 875 m
2 Area of the hut
= 15 x 5
= 75 m
2 Area of the grass patch cannot be fed on
= 875 - 75 - 157.785
= 642.215 m
2 Answer(s): (a) 157.785 m
2; (b) 642.215 m
2