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The radius of a unicycle wheel is 1 foot. When the unicycle travels

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The radius of a unicycle wheel is 1 foot. When the unicycle travels [#permalink]

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New post 20 Nov 2017, 00:18
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The radius of a unicycle wheel is 1 foot. When the unicycle travels continuously in one direction for 500 feet, the wheel makes v revolutions. Of the following, which is the best approximation to v?

(A) 80
(B) 160
(C) 310
(D) 3,140
(E) 6,280
[Reveal] Spoiler: OA

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The radius of a unicycle wheel is 1 foot. When the unicycle travels [#permalink]

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New post 20 Nov 2017, 00:23
v(2*pi* 1) = 500
v= 80 approx
--A--
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The radius of a unicycle wheel is 1 foot. When the unicycle travels [#permalink]

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New post 20 Nov 2017, 04:32
Bunuel wrote:
The radius of a unicycle wheel is 1 foot. When the unicycle travels continuously in one direction for 500 feet, the wheel makes v revolutions. Of the following, which is the best approximation to v?

(A) 80
(B) 160
(C) 310
(D) 3,140
(E) 6,280


Radius = 1 foot

Distance travelled = 500 feet

Total Number of revolutions = v

Total Distance travelled = Distance travelled in 1 Revolution * Number of revolutions

Also, Distance travelled in 1 revolution = Circumference of the wheel = 2*π*r = 2π

500 = 2π * v

i.e. v = 500/2π = 79.57 = 80

Answer: Option A
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Last edited by GMATinsight on 20 Nov 2017, 07:14, edited 2 times in total.

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Re: The radius of a unicycle wheel is 1 foot. When the unicycle travels [#permalink]

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New post 20 Nov 2017, 04:57
GMATinsight wrote:
Radius = 1 foot

Distance travelled = 500 feet

Total Number of revolutions = v

Total Distance travelled = Distance travelled in 1 Revolution * Number of revolutions

Also, Distance travelled in 1 revolution = Circumference of the wheel = 2*π*r = 2π

Total Distance travelled =v = 2π * 500= 3140

Answer: Option D

Would you please explain the highlighted part?
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The radius of a unicycle wheel is 1 foot. When the unicycle travels [#permalink]

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New post 20 Nov 2017, 05:42
TaN1213 wrote:
GMATinsight wrote:
Radius = 1 foot

Distance travelled = 500 feet

Total Number of revolutions = v

Total Distance travelled = Distance travelled in 1 Revolution * Number of revolutions

Also, Distance travelled in 1 revolution = Circumference of the wheel = 2*π*r = 2π

Total Distance travelled =v = 2π * 500= 3140

Answer: Option D

Would you please explain the highlighted part?



Circumference= 2π
No. Of revolutions= v

Total Distance travelled = Distance travelled in 1 Revolution * Number of revolutions

I.e. 500 = 2π*v i.e. v = 80

I hope it helps!!! :)

Posted from my mobile device
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Last edited by GMATinsight on 20 Nov 2017, 07:15, edited 1 time in total.

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Re: The radius of a unicycle wheel is 1 foot. When the unicycle travels [#permalink]

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New post 20 Nov 2017, 05:47
GMATinsight wrote:
TaN1213 wrote:
GMATinsight wrote:
Radius = 1 foot

Distance travelled = 500 feet

Total Number of revolutions = v

Total Distance travelled = Distance travelled in 1 Revolution * Number of revolutions

Also, Distance travelled in 1 revolution = Circumference of the wheel = 2*π*r = 2π

Total Distance travelled =v = 2π * 500= 3140

Answer: Option D

Would you please explain the highlighted part?



Circumference= 2π
No. Of revolutions= 500

Total Distance travelled = Distance travelled in 1 Revolution * Number of revolutions

I.e. total distance = 2π*500 = 1000π= 1000*3.14= 3140

I hope it helps!!! :)

Posted from my mobile device


Please note that the number of revolutions is “v” and not 500. 500 is the distance travelled and hence we have to find the revolutions. Hence v=500/(2.pi)
~80. Option A

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The radius of a unicycle wheel is 1 foot. When the unicycle travels [#permalink]

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New post 20 Nov 2017, 05:49
GMATinsight wrote:

Circumference= 2π
No. Of revolutions= 500

Total Distance travelled = Distance travelled in 1 Revolution * Number of revolutions

I.e. total distance = 2π*500 = 1000π= 1000*3.14= 3140

I hope it helps!!! :)

Posted from my mobile device


No. Of revolutions= v --- as per the question and we need to find 'v' not the total distance traveled (if that's not stated by the fact given in the question that distance is 500)
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Re: The radius of a unicycle wheel is 1 foot. When the unicycle travels [#permalink]

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New post 20 Nov 2017, 06:02
If the radius is 1 foot, the circumference of the wheel is 2*radius*pi, which is 2*pi which is approximately 6.28.

If it travels 500 feet, and you want the revolutions, 500/6.28 is approximately 79.6, which should get answer A.

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Re: The radius of a unicycle wheel is 1 foot. When the unicycle travels [#permalink]

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New post 22 Nov 2017, 11:09
Bunuel wrote:
The radius of a unicycle wheel is 1 foot. When the unicycle travels continuously in one direction for 500 feet, the wheel makes v revolutions. Of the following, which is the best approximation to v?

(A) 80
(B) 160
(C) 310
(D) 3,140
(E) 6,280


Since the radius of the wheel is 1 foot, the circumference is 2π(1) ≈ 3.14 x 2 = 6.28 ≈ 6

So in 500 feet, the wheel makes approximately 500/6 = 83.33 or about 80 revolutions.

Answer: A
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Re: The radius of a unicycle wheel is 1 foot. When the unicycle travels   [#permalink] 22 Nov 2017, 11:09
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