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primary 6 | Maths
| Geometry
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Date Posted: 1 year ago
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thank you
the leash cannot pass through the walls of the house, unless the leash is made of "anti-matter".
sorry, am not able to draw diagram in this comment box, so have to try to describe the situation with the aid of the diagram on the left ...
firstly, consider the bottom right of the house as the center of a clock. the dog can reach an area which is 3/4 of a circle of radius of 30m, and direction stretches from the 12 o'clock to the 9 o'clock direction out from the bottom right of the house.
next, consider when the dog has gone in the 12 o'clock direction from the bottom right corner of the house. now, from the top right corner of the house, the dog has 14m of leash left. the dog can further reach an area which is 1/4 of a circle of radius 14m, and direction stretches from the 9 o'clock to the 12 o'clock direction out from the top right of the house.
finally, consider when the dog has gone in the 9 o'clock direction from the bottom right corner of the house. now, from the bottom left corner of the house, the dog has 14m of leash left. the dog can reach an area which is 1/4 of a circle of radius 14m, and direction stretches from the 9 o'clock to the 12 o'clock direction out from the bottom left of the house.
total area that dog can reach
= (3/4) x pi x 30 x 30 + 2 x (1/4) x pi x 14 x 14
= 2427.22 m2.
sorry, am not able to draw diagram in this comment box, so have to try to describe the situation with the aid of the diagram on the left ...
firstly, consider the bottom right of the house as the center of a clock. the dog can reach an area which is 3/4 of a circle of radius of 30m, and direction stretches from the 12 o'clock to the 9 o'clock direction out from the bottom right of the house.
next, consider when the dog has gone in the 12 o'clock direction from the bottom right corner of the house. now, from the top right corner of the house, the dog has 14m of leash left. the dog can further reach an area which is 1/4 of a circle of radius 14m, and direction stretches from the 9 o'clock to the 12 o'clock direction out from the top right of the house.
finally, consider when the dog has gone in the 9 o'clock direction from the bottom right corner of the house. now, from the bottom left corner of the house, the dog has 14m of leash left. the dog can reach an area which is 1/4 of a circle of radius 14m, and direction stretches from the 9 o'clock to the 12 o'clock direction out from the bottom left of the house.
total area that dog can reach
= (3/4) x pi x 30 x 30 + 2 x (1/4) x pi x 14 x 14
= 2427.22 m2.
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