On a rectangular plot, a horse is tied to a pole at a corner of a hut which measures 24 m by 8 m. The hut is at the centre of the rectangular grass patch and there is a 16 m wide border of grass patch around it. Given that the rope is 12 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 = 12 m
Length of the rope that covers the remaining area which is
14 of the small circle
= 12 - 8
= 4 m
Maximum area that the horse can feed on
= (
34 x π x 12 x 12) + (
14 x π x 4 x 4)
= 112π
= 351.68 m
2 (b)
Length of the rectangular plot
= 24 + (2 x 16)
= 24 + 32
= 56 m
Breadth of the rectangular plot
= 8 + (2 x 16)
= 8 + 32
= 40 m
Area of the rectangular plot
= 56 x 40
= 2240 m
2 Area of the hut
= 24 x 8
= 192 m
2 Area of the grass patch cannot be fed on
= 2240 - 192 - 351.68
= 1696.32 m
2 Answer(s): (a) 351.68 m
2; (b) 1696.32 m
2