EvaJager wrote:

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.

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.