half cone

[shahar]

In which methods can I solve it:

Before you have 4 cones. Which one of them is "half full"?
The text in the source:
לפניכם ארבעה חרוטים. איזה מהם "מלא למחצה"? נמקו
א=(a)
ב=(b)
ג=(c)
ד=(d)
How I explains why ("נמקו"[=You must to give a reason"])?

 

[The Highlander]

In which methods can I solve it:
View attachment 39989
Before you have 4 cones. Which one of them is "half full"?
The text in the source:
לפניכם ארבעה חרוטים. איזה מהם "מלא למחצה"? נמקו
א=(a)
ב=(b)
ג=(c)
ד=(d)
How I explains why ("נמקו"[=You must to give a reason"])?

Hi @shahar

I suspect the answer will be: ד=(d), as the cone needs to be just over 79% full for it to be "half full" (by volume).

The explanation isn't particularly simple but if you wish to explore it to see if you can prepare your own explanation you might want to have a look here (and/or maybe watch the video below).

​

By the way, did you look at the material I posted for you in your previous thread here (qv)? You never came back to say whether you were able to complete the task (or comment on the materials suggested).

Hope that helps.

 

[Dr.Peterson]

In which methods can I solve it:
View attachment 39989
Before you have 4 cones. Which one of them is "half full"?
The text in the source:
לפניכם ארבעה חרוטים. איזה מהם "מלא למחצה"? נמקו
א=(a)
ב=(b)
ג=(c)
ד=(d)
How I explains why ("נמקו"[=You must to give a reason"])?

Here is Google's translation:

​

For a quick explanation: All cones in the picture are similar (because angles are the same), so volumes are proportional to the cube of linear measures (such as depth).

So in order for the ratio of volumes (liquid to container) to be 1:2, the depths must have a ratio of [imath]1:\sqrt[3]{2} = 1:1.26 = 0.7937:1[/imath]. The closest to this is (d), which is actually more precise than I expected:

​