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705-805 (Hard)|   Geometry|      
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EvaJager
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Helga and Rob like corn on cob. Each prefers to eat the gene 06 Aug 2012, 05:46
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85% (hard)

Question Stats:

52% (02:45) correct 48% (02:32) wrong based on 226 sessions

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Helga and Rob like corn on the cob. Each prefers to eat the genetically modified type corn, which has perfect cylindrical shape.
Helga likes to eat her corn by chewing circular strips of equal width. Rob prefers to go along the height of the cylinder, munching straight strips of the same width as Helga's strips. If Helga eats half as many circular strips as Rob eats straight strips, what is the ratio between the height and the radius of the corn on the cob?

\((A)\, 1:2\)
\((B)\, 2:1\)
\((C)\, 1:\pi\)
\((D)\, \pi:1\)
\((E)\, 1:\sqrt{\pi}\)
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D
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Helga and Rob like corn on cob. Each prefers to eat the gene 06 Aug 2012, 06:04
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EvaJager
Helga and Rob like corn on cob. Each prefers to eat the genetically modified type corn, which has perfect cylindrical shape.
Helga likes to eat her corn by chewing circular strips of equal width. Rob prefers to go along the height of the cylinder, munching straight strips of the same width as Helga's strips. If Helga eats half as many circular strips as Rob eats straight strips, what is the ratio between the height and the radius of the corn on cob?

\((A)\, 1:2\)
\((B)\, 2:1\)
\((C)\, 1:\pi\)
\((D)\, \pi:1\)
\((E)\, 1:\sqrt{\pi}\)
Show more

Say the the width of the strip each eats is \(x\).

Since Helga eats the corn circularly, then the number of strips she eats is \(\frac{h}{x}\).
Since Rob eats the corn along the height, then the number of strips he eats is \(\frac{2\pi{r}}{x}\).

We are told that \(\frac{h}{x}=\frac{1}{2}*\frac{2\pi{r}}{x}\) --> \(\frac{h}{r}=\pi\).

Answer: D.
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Helga and Rob like corn on cob. Each prefers to eat the gene 17 Aug 2012, 20:55
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Bunuel
EvaJager
Helga and Rob like corn on cob. Each prefers to eat the genetically modified type corn, which has perfect cylindrical shape.
Helga likes to eat her corn by chewing circular strips of equal width. Rob prefers to go along the height of the cylinder, munching straight strips of the same width as Helga's strips. If Helga eats half as many circular strips as Rob eats straight strips, what is the ratio between the height and the radius of the corn on cob?

\((A)\, 1:2\)
\((B)\, 2:1\)
\((C)\, 1:\pi\)
\((D)\, \pi:1\)
\((E)\, 1:\sqrt{\pi}\)

Say the the width of the strip each eats is \(x\).

Since Helga eats the corn circularly, then the number of strips she eats is \(\frac{h}{x}\).
Since Rob eats the corn along the height, then the number of strips he eats is \(\frac{2\pi{r}}{x}\).

We are told that \(\frac{h}{x}=\frac{1}{2}*\frac{2\pi{r}}{x}\) --> \(\frac{h}{r}=\pi\).

Answer: D.
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Please explain how you obtained the number of strips eaten by each of them; how was the equality obtained? How can we use the information about the way of their eating corn to determine the number of strips eaten by each of them.
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Helga and Rob like corn on cob. Each prefers to eat the gene 20 Aug 2012, 10:51
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The circumference of the cylinder is 2*pi*r.
Dividing by x gives the number of vertical strips ,because each strip is of width x.
The height of the cylinder is h.Dividing by x will give you the number of horizontal strips.
Now apply the data given in the question and equate.
Hope this helps .
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Helga and Rob like corn on cob. Each prefers to eat the gene 08 Jun 2018, 01:18
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EvaJager
Helga and Rob like corn on the cob. Each prefers to eat the genetically modified type corn, which has perfect cylindrical shape.
Helga likes to eat her corn by chewing circular strips of equal width. Rob prefers to go along the height of the cylinder, munching straight strips of the same width as Helga's strips. If Helga eats half as many circular strips as Rob eats straight strips, what is the ratio between the height and the radius of the corn on the cob?

\((A)\, 1:2\)
\((B)\, 2:1\)
\((C)\, 1:\pi\)
\((D)\, \pi:1\)
\((E)\, 1:\sqrt{\pi}\)
Show more


Let r be the radius & h be the height of the cylindrical corn cob.

Total Curved Surface Area = \(2*\pi*r*h\)

Let \(a\) be the width of each strip.

Curved Surface Area of each strip eaten by Helga = \(2*\pi*r*a\)

Hence # of strips eaten by Helga, \(S_h\) = \((2*\pi*r*h)\)/\((2*\pi*r*a)\) = \(h/a\)

Area of each strip eaten by Rob = \(h * a\)

Hence # of Strips eaten by Rob, \(S_r\) = \(2*\pi*r*h\)/\(h * a\) = \(2*\pi*r/a\)

Now given that, \(S_h\) = \({S_r}/2\)

Hence, \(h/a\) = \(2*\pi*r/{2a}\)

Simplified as, \(h/r\) = \(\pi\)

Answer D.

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GyM
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Helga and Rob like corn on cob. Each prefers to eat the gene 23 Jun 2019, 08:13
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Bunuel
EvaJager
Helga and Rob like corn on cob. Each prefers to eat the genetically modified type corn, which has perfect cylindrical shape.
Helga likes to eat her corn by chewing circular strips of equal width. Rob prefers to go along the height of the cylinder, munching straight strips of the same width as Helga's strips. If Helga eats half as many circular strips as Rob eats straight strips, what is the ratio between the height and the radius of the corn on cob?

\((A)\, 1:2\)
\((B)\, 2:1\)
\((C)\, 1:\pi\)
\((D)\, \pi:1\)
\((E)\, 1:\sqrt{\pi}\)

Say the the width of the strip each eats is \(x\).

Since Helga eats the corn circularly, then the number of strips she eats is \(\frac{h}{x}\).
Since Rob eats the corn along the height, then the number of strips he eats is \(\frac{2\pi{r}}{x}\).

We are told that \(\frac{h}{x}=\frac{1}{2}*\frac{2\pi{r}}{x}\) --> \(\frac{h}{r}=\pi\).

Answer: D.
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I have a doubt here.How did you come to know that the rob's number of strips will be 2*pi*r/x ? We dont know how the strips are being cut here.It will be 2r/x if the strips are cut from a circle side wise. if the strips are cut till the center then it will be 2*pi*r/x.Please expain.
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Helga and Rob like corn on cob. Each prefers to eat the gene 02 Sep 2020, 07:19
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EvaJager
Helga and Rob like corn on the cob. Each prefers to eat the genetically modified type corn, which has perfect cylindrical shape.
Helga likes to eat her corn by chewing circular strips of equal width. Rob prefers to go along the height of the cylinder, munching straight strips of the same width as Helga's strips. If Helga eats half as many circular strips as Rob eats straight strips, what is the ratio between the height and the radius of the corn on the cob?

\((A)\, 1:2\)
\((B)\, 2:1\)
\((C)\, 1:\pi\)
\((D)\, \pi:1\)
\((E)\, 1:\sqrt{\pi}\)
Show more
Solution:

Let the radius and height of the cob be r and h, respectively. Let the number of circular strips Helga eats be n. Then, Rob eats 2n straight strips.

Let the width of each circular strip and each horizontal strip be w. Then, the height of the cob is nw and the circumference of the base is 2nw. We have:

h = nw

2?r = 2nw

From the second equation, we obtain nw = ?r. Substituting nw = h, we obtain h = ?r. Thus, h/r = ?. The ratio of the height to the radius is ? : 1.

Answer: D
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Helga and Rob like corn on cob. Each prefers to eat the gene 06 Feb 2022, 01:02
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EvaJager
Helga and Rob like corn on the cob. Each prefers to eat the genetically modified type corn, which has perfect cylindrical shape.
Helga likes to eat her corn by chewing circular strips of equal width. Rob prefers to go along the height of the cylinder, munching straight strips of the same width as Helga's strips. If Helga eats half as many circular strips as Rob eats straight strips, what is the ratio between the height and the radius of the corn on the cob?

\((A)\, 1:2\)
\((B)\, 2:1\)
\((C)\, 1:\pi\)
\((D)\, \pi:1\)
\((E)\, 1:\sqrt{\pi}\)
Show more

let the height and width be H and w

1/2 * 2*pi *r *w = H* w
=> H/r =pi

THerefore IMO D
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Helga and Rob like corn on cob. Each prefers to eat the gene 31 Jul 2023, 17:30
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