Answer:
1: 45*pi meters for 1 revolution
2: 32/175 of an hour or about .183 of an hour
3: 7875*pi/32 meters per hour
Step-by-step explanation:
To find the distance around a circle it's just the circumference. What is the formula for circumference? 2*pi*r. Do we have the radius? not exactly, but we have the diameter. radius is .5*diameter, so radius is .5*45m = 22.5 m Now, the circumference is 2*pi*r = 45*pi. Fun fact, 2*pi is the diameter, so you could have just plugged that in instead.
B is kinda complicated. We need to find how long it takes to make one revolution. The question tells us 700 people will get on, go around 1 full revolution then get off in one hour. It also tells us there are 32 cars, each that seats 4 people so the whole wheel can hold a total of 128. So each revolution carries 128 people around. 1 revolution takes 128, 2 takes 256, 3 takes 384, 4 takes 512, 5 takes 640 and 6 takes 768, so it will be somewhere between 5 and 6 revolutions per hour. Now how do we find it exactly?
There are 32 cars, so if we split a circle with 32 parts means there is 360/32 = 11.25 degrees between each car. now, it says 700 people an hour can ride it. if each car holds 4 people we divide 700 by 4 and get 175 cars pass the entrance in an hour. Or in other words if you sat by the entrance and count how many times people get on you will get to 175. if there are 32 cars we are going to be counting some twice. to find how many we divide 175 by 32 and get 5.46875. That means we are going to count each car 5 times at least and some 6 times. Between 5 and 6, so that sounds right.
Let's fgure out how many are counted 6 times by handling the math a little differently. 175/32 and from that we take away 5 so 175/35-5
175/32 - 5
175/32 - 160/32
15/32
That means the first through 15th car are counted 6 times, then the 16th through 32nd are counted once. So that's 5 full revolutions plus however much it takes to get to the 15th car. Now how much is that? well each car has 11.25 degrees between it , so that's 15*11.25 = 168.75. That's almost 180 degrees, which is half a rotation, which makes sense because 15 is almost half of 32.
NOW! we have the amount of rotation in an hour is 5 and 15/32 rotations in 1 hour. Now, let's change this so we have 1 rotation. If we divide both by 5 15/32 we get the time for 1 rotation.
5 15/32 rotations per 1 hour
(5 15/32)/(5 15/32) rotations per 1/(5 15/32) hours
1 rotation 32/175 hour or about .183 of an hour.
I would use the fraction so it's an exact answer. Let me know if you have trouble following it because it was super long and pretty complicated
3. So this was solved mostly in part 2, so maybe there was an easier way to solve it that I overlooked. Still, the answer was gotten, and I'd be happy to explain anything needed. Anyway, the speed is the distance that moves. the revolutions per hour is 5 15/32 rotations per hour or 175/32 rotations per hour. Each rotation moves the ferris wheel one circumference. What is the circumference? This was in part 1, 45*pi. so that means 45*pi per revolution and there are 175/32 revolutions per hour. that means 45*pi*175/32 meters per hour or 7875*pi/32 meters per hour. If you need this in different units and you need help let me know if you need help with that.
Again, let me know if you need any more explanation.
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