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lions [1.4K]
3 years ago
5

If the length of the minute hand of the clock in London commonly known as “Big Ben” is 11.25’ from the center of the clock to th

e tip of the hand, what is the area swept out by the minute hand as it moves 5 minutes of time?
A) 10.55 ft2
B) 28.13 ft2
C) 33.13 ft2
D) 66.27 ft2
Mathematics
1 answer:
rodikova [14]3 years ago
5 0
First, we should figure out the area of the entire face of the clock because we need that information to solve the problem. The formula for the area of a circle is A=pi*r^2. Since we know that r (radius) is equal to 11.25 feet, we can plug this in for r and solve for A: A=pi*11.25^2 which equals A=397.61 ft^2 rounded to the nearest hundredth. 

Now, to find the area the hand sweeps over in 5 minutes, we should determine how much of the clock the hand sweeps over in 5 minutes. Think about it like this: since 5 minutes goes into 60 minutes 12 times (60/5=12), then 5 minutes is one twelfth of the clock's face. Therefore, we are going to divide the total area by 12 (397.61/12) to get 33.13 ft^2, so the answer is C.

I hope this helps.
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