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A dog is attached to a 35​-foot rope fastened to the outside corner of a​ fenced-in garden that measures 28 feet by 36 feet. Assuming that the dog cannot enter the​ garden, compute the exact area that the dog can wander.

The dog can wander an area of ___ square feet
(exact answer, using the pi symbol)


Sagot :

The area that the dog can wander based on the information provided will be 931Ï€.

How to calculate the area?

From the information, we are told that the dog dog is attached to a 35-foot rope fastened to the outside corner of a fenced-in garden that measures 28 feet by 36 feet.

In this case, the dog is in an outside corner. The dog can trace 3/4 of a circle when it starts walking in a circle away form the wall.

The area that the dog can wander will be:

= 3/4(π35²) + 1/4(π(35 - 28)²)

= 3/4π(35)² + 1/4π(7)²

= (3/4 × 1225)π + (1/4 × 49)π

= 918.75Ï€ + 12.25Ï€

= 931Ï€

Therefore, the area that the dog can wander based on the information provided will be 931Ï€.

Learn more about area on:

brainly.com/question/25292087

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