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# In the figure above, AB represents a ramp and the circle represents a

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Math Expert
Joined: 02 Sep 2009
Posts: 51107
In the figure above, AB represents a ramp and the circle represents a  [#permalink]

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23 Nov 2017, 22:29
00:00

Difficulty:

(N/A)

Question Stats:

75% (01:16) correct 25% (01:41) wrong based on 25 sessions

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In the figure above, AB represents a ramp and the circle represents a wheel that has radius 1.5 feet. If the wheel is rolled up the top of the ramp, which of the following is closest to the number of revolutions it will make?

(A) 1 2/3
(B) 2
(C) 3 1/2
(D) 5
(E) 10

Attachment:

2017-11-23_2026_001.png [ 6.52 KiB | Viewed 490 times ]

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Re: In the figure above, AB represents a ramp and the circle represents a  [#permalink]

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24 Nov 2017, 00:09
Bunuel wrote:
In the figure above, AB represents a ramp and the circle represents a wheel that has radius 1.5 feet. If the wheel is rolled up the top of the ramp, which of the following is closest to the number of revolutions it will make?

(A) 1 2/3
(B) 2
(C) 3 1/2
(D) 5
(E) 10

Attachment:
2017-11-23_2026_001.png

Circumference of circle = 2 * pie * r = 3* pie
Distance = 15
Revolutions = 15/3*pie = 35/22 = ~1 2/3

A
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Luckisnoexcuse

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Joined: 22 May 2016
Posts: 2204
Re: In the figure above, AB represents a ramp and the circle represents a  [#permalink]

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24 Nov 2017, 09:11
1
Bunuel wrote:
In the figure above, AB represents a ramp and the circle represents a wheel that has radius 1.5 feet. If the wheel is rolled up the top of the ramp, which of the following is closest to the number of revolutions it will make?

(A) 1 2/3
(B) 2
(C) 3 1/2
(D) 5
(E) 10

Attachment:
2017-11-23_2026_001.png

In distance, D, problems with wheels and number of revolutions:

D = (circumference, c) * (# of revolutions), so

# of revolutions = $$\frac{D}{c}$$

D = ramp AB length = hypotenuse
The 3x-4x-5x right triangle has multiplier of 3:
(5*3)= 15 = ramp AB length = D*

Circumference of wheel A
2πr = 2π(1.5) = 3π
$$c = (3)(3.14)\approx{9.4}$$

# revolutions =
$$\frac{D}{c}=\frac{15}{9.4}\approx{1.59}$$, or $$1.6$$

Bunuel , the first image of the figure does not show up, though the one in the spoiler does. I tried two browsers.

*OR Pythagorean theorem, $$9^2 + 12^2 = h^2$$
$$81 + 144 = 225 = h^2$$
$$\sqrt{h^2}=\sqrt{225}$$ , so $$h=15$$
Math Expert
Joined: 02 Sep 2009
Posts: 51107
Re: In the figure above, AB represents a ramp and the circle represents a  [#permalink]

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24 Nov 2017, 09:14
genxer123 wrote:
Bunuel wrote:
In the figure above, AB represents a ramp and the circle represents a wheel that has radius 1.5 feet. If the wheel is rolled up the top of the ramp, which of the following is closest to the number of revolutions it will make?

(A) 1 2/3
(B) 2
(C) 3 1/2
(D) 5
(E) 10

Attachment:
2017-11-23_2026_001.png

In distance, D, problems with wheels and number of revolutions:

D = (circumference, c) * (# of revolutions), so

# of revolutions = $$\frac{D}{c}$$

D = ramp AB length = hypotenuse
The 3x-4x-5x right triangle has multiplier of 3:
(5*3)= 15 = ramp AB length = D*

Circumference of wheel A
2πr = 2π(1.5) = 3π
$$c = (3)(3.14)\approx{9.4}$$

# revolutions =
$$\frac{D}{c}=\frac{15}{9.4}\approx{1.59}$$, or $$1.6$$

Bunuel , the first image of the figure does not show up, though the one in the spoiler does. I tried two browsers.

*OR Pythagorean theorem, $$9^2 + 12^2 = h^2$$
$$81 + 144 = 225 = h^2$$
$$\sqrt{h^2}=\sqrt{225}$$ , so $$h=15$$

_______________
Edited. Thank you.
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Re: In the figure above, AB represents a ramp and the circle represents a &nbs [#permalink] 24 Nov 2017, 09:14
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