On a rectangular plot, a horse is tied to a pole at a corner of a hut which measures 39 m by 13 m. The hut is at the centre of the rectangular grass patch and there is a 26 m wide border of grass patch around it. Given that the rope is 23 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 = 23 m
Length of the rope that covers the remaining area which is
14 of the small circle
= 23 - 13
= 10 m
Maximum area that the horse can feed on
= (
34 x π x 23 x 23) + (
14 x π x 10 x 10)
= 421.75π
= 1324.295 m
2 (b)
Length of the rectangular plot
= 39 + (2 x 26)
= 39 + 52
= 91 m
Breadth of the rectangular plot
= 13 + (2 x 26)
= 13 + 52
= 65 m
Area of the rectangular plot
= 91 x 65
= 5915 m
2 Area of the hut
= 39 x 13
= 507 m
2 Area of the grass patch cannot be fed on
= 5915 - 507 - 1324.295
= 4083.705 m
2 Answer(s): (a) 1324.295 m
2; (b) 4083.705 m
2