On a rectangular plot, a horse is tied to a pole at a corner of a hut which measures 42 m by 14 m. The hut is at the centre of the rectangular grass patch and there is a 28 m wide border of grass patch around it. Given that the rope is 24 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 = 24 m
Length of the rope that covers the remaining area which is
14 of the small circle
= 24 - 14
= 10 m
Maximum area that the horse can feed on
= (
34 x π x 24 x 24) + (
14 x π x 10 x 10)
= 457π
= 1434.98 m
2 (b)
Length of the rectangular plot
= 42 + (2 x 28)
= 42 + 56
= 98 m
Breadth of the rectangular plot
= 14 + (2 x 28)
= 14 + 56
= 70 m
Area of the rectangular plot
= 98 x 70
= 6860 m
2 Area of the hut
= 42 x 14
= 588 m
2 Area of the grass patch cannot be fed on
= 6860 - 588 - 1434.98
= 4837.02 m
2 Answer(s): (a) 1434.98 m
2; (b) 4837.02 m
2