A record playa with a speed of 33 1/3 revolutions per minute, meaning that a needle in a groove around te edge of the record will make 33 and 1/3 circuits around the record in one minute. If the diameter of the record is 40 centimeters, how many centimeters does the needle travel in one minute?
A. 400
B. 1333 1/3
C. 2000
D. 2400
E. 2666 2/3
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To find the distance traveled by the needle in one minute, we first need to calculate the circumference of the record.
The formula for the circumference of a circle is C = πd, where C represents the circumference and d represents the diameter.
In this case, the diameter of the record is given as 40 centimeters. So, the circumference of the record is:
C = π * 40 = 40π centimeters.
Since the needle makes 33 1/3 circuits in one minute, it travels a total distance of 33 1/3 times the circumference of the record.
To calculate the distance traveled by the needle in one minute:
Distance = 33 1/3 * 40π
= (100/3) * 40π
= (100 * 40 * π) / 3
≈ 1333 1/3 * π
Now, to find the answer in centimeters, we need to multiply 1333 1/3 with π (approximately 3.14159):
1333 1/3 * 3.14159 ≈ 4199.99
Therefore, the needle travels approximately 4200 centimeters in one minute.
Since none of the answer choices exactly matches 4200, we need to find the closest option:
A. 400 - Too small
B. 1333 1/3 - Too small
C. 2000 - Too small
D. 2400 - Too small
E. 2666 2/3 - Too small
None of the answer choices are accurate, but the closest one is option D: 2400 centimeters.