Youre driving your car along a circular track of a radius of 2 miles. Given that you traverse 1/8 of the track

Question

(Cont...)
In 7 minutes and that your wheels make 3500 revolutions per minute. What is the radius of the tires?

Answer 1

track circumference = 2 * pi * r
segment driven = track circumference / 8
tire revolutions made so far = 7 * 3500

segment driven = pi / 2 miles
tire revolution made so far = 24500

circumference of tire = segment driven / tire revolution made so far
circumference of tire = pi / 49000 miles

radius of tire = circumference of tire / (2 * pi)
radius of tire = 1 / 98000 miles
radius of tire = 0.64653 inches

That is one VERY small tire.

Answer 2

Let's see:

If the wheel makes 3,500 revolutions per minute for 7 minutes, that means the circumference of the wheel goes around 24,500 times in seven minutes. Circumference = 2 x pi x r, so the total distance traveled by the wheel can be represented by 49,000 x pi x r.

On the other side of the equation, if the radius of the track is two miles, or 10,560 feet, and the wheel went 1/8 of the way around the circumference of the track, the distance traveled can be represented by 1/8 x 2 x pi x 10,560, or 2,640 x pi.

So let's simplify:

49,000 x pi x r = 2,640 x pi, so divide each side by pi

49,000 x r = 2,640, now you divide each side by 49,000

r = 2,640/49,000 = 0.05387 feet

Answer 3

Here are your steps:

1) find the length of the track, it's the circumference = 2*pi*radius.

2) divide by 8, that's 1/8 of the track, the distance you covered.

3) Distance = speed * time, so divide the distance by 7 minutes to get your speed in miles per minute.

4) Multiply by 5280 to convert the speed to feet per minute.

5) x feet/min = 3500 revs/min ---> x feet = 3500 revs ---> divide the result by 3500 to get the number of feet that are in one revilution.

6) You now have the circumference of the tires. C=2*pi*r, so divide by 2*pi to get the radius in feet. Multiply by 12 to convert to inches.

Answer 4

This one is ALL about units conversion!

First, some of the easy things: you travel the WHOLE track in 56 minutes.
At 3500 rpm, your tires have turned 56*3500 times. That is, the circumfrence of your tire is the length of the track divided by (56*3500).

The WHOLE track is 2*2*pi miles in length, in miles, but you probably want to make this in inches, since this is often what tire radii are measure in. The track length is then:

4.*pi*5280*12.

Therefore the circumfrence of your tire is
4*pi*12.*5280/(56*3500).
The RADIUS is the circumfrence divided by 2*pi, so the radius is

4*pi*12*5280/(5600*3500*2*pi)
which simplifies to
2*12*5280/(5600*3500)

Answer 5

1/8 of the track has a length of pi/4*radius, or 1.5707 miles.

The wheels turn 7*3500 revolutions over this distance.

The circumfrence of the tire must be 1.5707 miles / (7*3500) = .00006411 miles or 0.3385 feet or 4.06227 inches.

The radius of the tire would be the circumfrence divided by 2xpi, or 0.646 inches. That's a tiny tire! Did you give us the correct numbers?

Answer 6

circumference of the circular track = 2*pi*r
distance covered = 1/8*2*pi*r = pi/2miles = 1.5714miles

24500 revolutions by the tire in 7 minutes cover 1.5714 miles

1revolution covers 1.5714/24500 = 10.32cm

2*pi*r = 10.32cm

r = 1.64cm

The figure made me to verify my workout again and again

Answer 7

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Answer 8

radius of the track=2*5280 feet
=10560 feet
circumference=2*3.14
1/8th ofthis=2*3.14*10560/8
=2*3.14*1320 feet
speed per minute=2*3.14*1320/7ft/min
distance travelled in 3500 rev=2*3.14*1320/7 feet
if the radius is r"
2*3.14*r*3500=2*3.14*1320/7feet
=2*3.14*1320*12/7 inches
r=2*3.14*1320*12/7*3500*2*3.14
=0.647"