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A point on the edge of a fan blade that is rotating in a plane is 10 : Problem Solving (PS)
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# A point on the edge of a fan blade that is rotating in a plane is 10

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RAdius of the circular plane in which point travels is 10 cms
in one revolution = 20pie
in 15 seconds fan makes 75 revs (300*15/60)
So total distance = 75*20pie
1500 pie
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given data

60 seconds - 300 revolutions
15 seconds - 75 revolutions

distance travelled in 1 revolution = 2*pi*r
distance travelled in 75 revolutions = 150*pi*r
= 1500pi

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Revolutions /sec = 300/60 = 5
In 15 sec, revolutions = 15*5 = 75

distance traveled/ revolution = circumference = 2 * pi * (10)

Thus total distance in 15 sec = 2 * pi * (10) * 75

1800 * pi
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Re: A point on the edge of a fan blade that is rotating in a plane is 10 [#permalink]
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Hi All,

While this is an old post, it's a decent example of how the GMAT can test you on Geometry concepts using real-world items (and a story problem).

We're told that a fan blade is 10cm from the center of the fan (which means we have a radius of 10). We're then told that the fan blade spins for 15 seconds (which means that we're dealing with the circumference of a circle). We're asked how far the point "travels" if the fan makes 300 revolutions per minute.

The 'math' involved in this question can be done in a couple of different ways, but here's a step-by-step method that should be easy to follow:

Circumference = 2(pi)(R) = 2(pi)(10) = 20pi

So every revolution = 20pi cm traveled

15 seconds = 1/4 of a minute
(300 revolutions/minute)(1/4 of a minute) = 75 revolutions in 15 seconds

(20pi cm)(75) = 1500pi cm

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Re: A point on the edge of a fan blade that is rotating in a plane is 10 [#permalink]
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puma wrote:
A point on the edge of a fan blade that is rotating in a plane is 10 centimeters from the center of the fan. WHat is the distance traveled, in centimeters, by this point in 15 seconds when the fan runs at the rate of 300 revolutions per minutes?

A. 750pi
B. 1500pi
C. 1875pi
D. 3000pi
E. 7500pi

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Hope it helps.
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Re: A point on the edge of a fan blade that is rotating in a plane is 10 [#permalink]
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Hi,
what would be the level of this question ?
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Re: A point on the edge of a fan blade that is rotating in a plane is 10 [#permalink]
Benacher07 wrote:
Hi,
what would be the level of this question ?

You can check the difficulty level in the tags above the first post. It is based on the stats which are also given in the first post. So, as you can see it's 600-700 level question.
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Re: A point on the edge of a fan blade that is rotating in a plane is 10 [#permalink]
When given the speed in revolutions, the distance traveled will be speed * circumference
Here, the distance in 60 seconds = $$300 * 2*\pi*10$$
Hence the distance traveled in 15 seconds = $$\frac{15}{60}$$ * $$300 * 2*\pi*10$$ = $$1500\pi$$

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Re: A point on the edge of a fan blade that is rotating in a plane is 10 [#permalink]
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puma wrote:
A point on the edge of a fan blade that is rotating in a plane is 10 centimeters from the center of the fan. WHat is the distance traveled, in centimeters, by this point in 15 seconds when the fan runs at the rate of 300 revolutions per minutes?

A. 750pi
B. 1500pi
C. 1875pi
D. 3000pi
E. 7500pi

One entire revolution is equal to the circumference of the circle, which is 2 x π x 10 = 20π.

We must convert 300 revolutions per minute to revolutions per second: 300/60 = 5 revolutions per second. So in 15 seconds the number of revolutions is 5 x 15 = 75 revolutions.

So the total distance traveled is 20π x 75 = 1500π.

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Re: A point on the edge of a fan blade that is rotating in a plane is 10 [#permalink]
As usual from me, an alternative reasoning, however it can prove very useful and quick when needed:

You can imagine the fan blades inside the fan in your head, which basically comes back to draw a circle with the edge being a point at the edge of the circle!

2nd step: You can now deduct from the given info that the radius (distance from the edge of circle to the center of the circle) is of 10cm, with the perimeter being 2d=20cm!

3rd step: You can deduct that revolution=complete travel of the circle's area by the fan blade, at the rhythm of 300r/minute. You can also deduct that 15 seconds is 1/4 of a minute!

4th step: We combine all the info given and deducted to arrive at 300revolution x 20cm (diameter)=6000revolutions/minute, but we're only interested in 15 seconds, or 1/4 of a minute so 1/4th of 6000, which is equal to...1500!

The complete calculus is: 300 x 20=6000/4=1500

Answer B for the win! Hope this was useful!
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Re: A point on the edge of a fan blade that is rotating in a plane is 10 [#permalink]
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A point on the edge of a fan blade that is rotating in a plane is 10 centimeters from the center of the fan. WHat is the distance traveled, in centimeters, by this point in 15 seconds when the fan runs at the rate of 300 revolutions per minutes?

A point on the edge of a fan blade that is rotating in a plane denoted the radius of the fan = 10 cm
1 resolution = 1 complete circumference of the circle/fan
300 resolutions per min = 300/60= 5 res/sec
in 15 sec, total res = 5X15= 75
Distance covered in 15 secs= 75 X 2 X pi X 10 = 1500 pi
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Re: A point on the edge of a fan blade that is rotating in a plane is 10 [#permalink]
A point on the edge of a fan blade that is rotating in a plane is 10 centimeters from the center of the fan. WHat is the distance traveled, in centimeters, by this point in 15 seconds when the fan runs at the rate of 300 revolutions per minutes?

A. 750pi
B. 1500pi
C. 1875pi
D. 3000pi
E. 7500pi

We are told the radius = r = 10 --> C = 20pi

R = 300 revolutions / min so 15 seconds is the equivalent of 75 revolutions

75 x 20 pi = 1500pi

B.
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Re: A point on the edge of a fan blade that is rotating in a plane is 10 [#permalink]
To solve this problem, we need to find the distance traveled by the point on the fan blade in 15 seconds.

First, let's convert the given rate of 300 revolutions per minute to revolutions per second:

300 revolutions per minute = 300/60 = 5 revolutions per second.

Since the point on the fan blade is 10 centimeters from the center, the distance traveled by the point in one revolution is equal to the circumference of a circle with a radius of 10 centimeters.

The circumference of a circle is given by the formula C = 2πr, where r is the radius. Therefore, the circumference in this case is:

C = 2π(10) = 20π centimeters.

In one revolution, the point travels a distance of 20π centimeters.

To find the distance traveled in 15 seconds, we multiply the distance traveled in one revolution by the number of revolutions in 15 seconds:

Distance traveled = 20π * 5 * 15 = 1500π centimeters.

Therefore, the distance traveled by the point in 15 seconds is 1500π centimeters, which corresponds to option (B).
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Re: A point on the edge of a fan blade that is rotating in a plane is 10 [#permalink]
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