Distance Traveled by a Minute Hand Suppose the tip of the minute ...

Question

Distance Traveled by a Minute Hand Suppose the tip of the minute hand of a clock is 3 in. from the center of the clock. For each duration, determine the distance traveled by the tip of the minute hand. Leave answers as multiples of  π .                                                                                                                                                                                                                                                                                                                                        
                                                                                                                                                                                                                                                                                                                                                                                        
  4.5 hr

Accepted Answer

Welcome back. I am so glad you're here. We're asked to calculate the distance covered by the minute hand of a clock for the following duration. If the distance of the tip of the minute hand from the center of the clock is six centimeters or in other words, our R is equal to six centimeters, the radius of our circle, write your answer in terms of pi and that duration that the minute hand is going around is for 6. hours. Our answer choices are answer choice, a 78 pi centimeters. Answer choice B 72 pi centimeters, answer choice C 80 pi centimeters and answer choice D 178 pi centimeters. Then we have a diagram with a clock face. All right. So we are trying to find the arc length of a sector of a circle. Even though we're going around this circle multiple times. We recall from previous lessons that that formula is S equals R theta and this is great because we know our RR here is six centimeters and we just need to multiply that by theta. Well, we know that our minute hand is going around for 6.5 hours, one full rotation around the clock is one hour. And it's going to do that multiplied by six. Since we're talking in terms of pi we'll look at our angle in terms of radiance and we know that one full rotation in radiance is two pi so we take that two pi multiplied by six and that gets us 12 pie. Now, we just need to add that half of a rotation for that other half of an hour. And oops, I overshot that a little bit. But so we've got half a rotation. We're taking one half of two pi or two pi multiplied by one half. And that's going to be just one pie. 12 pi plus pi is 13 pi. So our angle measurement here beta equals pi. We can plug that in to our equation. So s equals instead of R six centimeters multiplied by, instead of theta 13 pi and six multiplied by 13 is 78. So remembering we've got a pie and a centimeters. We've got 78 pie centimeters and we look at our answer choices and that matches with answer choice. A well done. We'll catch you on the next one.

Distance Traveled by a Minute Hand Suppose the tip of the minute hand of a clock is 3 in. from the center of the clock. For each duration, determine the distance traveled by the tip of the minute hand. Leave answers as multiples of π . 4.5 hr

Key Concepts

Circumference of a Circle

Revolutions and Time

Distance Calculation

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