A puppy is tied to a leash in a back yard. His leash is 3 meters long, and he runs around in circles pulling the leash as far as it can go. What is the approximate distance the puppy runs in one lap?
Responses
A between 18 and 19 metersbetween 18 and 19 meters
B between 20 and 21 metersbetween 20 and 21 meters
C between 17 and 18 metersbetween 17 and 18 meters
D between 13 and 14 metersbetween 13 and 14 meters
E between 15 and 16 meters
E between 15 and 16 meters
The puppy is tied to a 3-meter-long leash and runs around in a circle, which means the leash's length is the circle's radius. The distance the puppy runs in one lap is equivalent to the circle's circumference, which is 2πr, where r is the leash length.
So, in this case, the distance the puppy runs in one lap is approximately 2π(3) = 18.85 meters, which falls between options E, between 15 and 16 meters.
I apologize for the error in my previous response. The correct distance the puppy runs in one lap is equal to the circumference of the circle with a radius of 3 meters, which can be calculated using the formula:
C = 2πr
Here, r = 3 meters, so:
C = 2π(3) ≈ 18.85 meters
Therefore, the approximate distance the puppy runs in one lap is about 18.85 meters, which falls between options A, between 18 and 19 meters. Again, I apologize for any confusion caused by my previous response.
To calculate the approximate distance the puppy runs in one lap, we can use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius of the circle.
In this case, the puppy is tied to a leash that is 3 meters long. The leash forms a circle around the puppy as it runs. The radius of this circle is half the length of the leash, so the radius is 3/2 = 1.5 meters.
Using the formula for the circumference, we can calculate:
C = 2π(1.5)
C ≈ 9.42 meters
Therefore, the approximate distance the puppy runs in one lap is between 9.42 and 9.42 meters.
However, none of the given answer choices match this range. The closest option is E - between 15 and 16 meters, which is not an exact match but falls within a similar range.