On a rectangular plot, a horse is tied to a pole at a corner of a hut which measures 21 m by 7 m. The hut is at the centre of the rectangular grass patch and there is a 14 m wide border of grass patch around it. Given that the rope is 9 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 = 9 m
Length of the rope that covers the remaining area which is
14 of the small circle
= 9 - 7
= 2 m
Maximum area that the horse can feed on
= (
34 x π x 9 x 9) + (
14 x π x 2 x 2)
= 61.75π
= 193.895 m
2 (b)
Length of the rectangular plot
= 21 + (2 x 14)
= 21 + 28
= 49 m
Breadth of the rectangular plot
= 7 + (2 x 14)
= 7 + 28
= 35 m
Area of the rectangular plot
= 49 x 35
= 1715 m
2 Area of the hut
= 21 x 7
= 147 m
2 Area of the grass patch cannot be fed on
= 1715 - 147 - 193.895
= 1374.105 m
2 Answer(s): (a) 193.895 m
2; (b) 1374.105 m
2