BdMO(Divisional)
Forum rules
Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
Can you hlp me with these?
- Attachments
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- oil_drum.JPG (22.29KiB)Viewed 6975 times
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- cube-sphere.JPG (27.53KiB)Viewed 6975 times
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- 2 circle.JPG (16.07KiB)Viewed 6975 times
r@k€€/|/
Re: BdMO(Divisional)
Please create separate posts for each problem from the next time, and use better topic. No one might be interested in your topic if they just see "BdMO divisional" in your topic. I mean posting in this forum already made it it clear this the problems are from BdMO divisional.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Re: BdMO(Divisional)
Whoa! Slowly bro! Please be a bit patient. Someone will solve your problem. Anyway it is better to write the statement of your problem in the forum and attach the image.rakeen wrote:thnx for the RULES. But where's the solution!
It is hard to read most of the statements. (You hand writing is better than that of me, but the image quality are not good)
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.
Re: BdMO(Divisional)
Hints:
To problem 1:
(Ratio of heights or sides)^3 = Ratio of volumes.
Problem 2:
Probably you have made some typos or linguistic mistakes in stating the problem. If you find it difficult to translate a problem into English you may write it in Bengali.
The problem, I think, is wrong because a cylinder inside a sphere can never have radius equal to that of the sphere. You may wonder why? Look, the upper and lower base of cylinder is parallel, so a line that goes just midway along the cylinder will be a diameter of the sphere and the midpoint of it is the center of the sphere, say $O$. Join $O$ to the circumference (পরিধি) of the base of the cylinder at $P$. Drop a perpendicular from $O$ to the the base at $R$; I hope you understand $OP$ is the hypotenuse (অতিভূজ) of a right angle triangle (সমকোণী ত্রিভূজ) whose base (ভূমি) is $OR$, the radius of the base of the cylinder. Now $OP$ can never be equal to $OR$.
Problem 3:
$\triangle PAB$ and $\triangle PCD$ are similar and $\frac {\triangle PAB}{\triangle PCD} = \frac {YA}{XR}$
Problem 4:
Note that the cone has two similar triangle inside it. One is the cross section of the whole cone and another is the cross section of the part of the cone inside the cylinder. Find heights and volume of the different sections.
Try solving them now. Have I mentioned something that you don't know already?
To problem 1:
(Ratio of heights or sides)^3 = Ratio of volumes.
Problem 2:
Probably you have made some typos or linguistic mistakes in stating the problem. If you find it difficult to translate a problem into English you may write it in Bengali.
The problem, I think, is wrong because a cylinder inside a sphere can never have radius equal to that of the sphere. You may wonder why? Look, the upper and lower base of cylinder is parallel, so a line that goes just midway along the cylinder will be a diameter of the sphere and the midpoint of it is the center of the sphere, say $O$. Join $O$ to the circumference (পরিধি) of the base of the cylinder at $P$. Drop a perpendicular from $O$ to the the base at $R$; I hope you understand $OP$ is the hypotenuse (অতিভূজ) of a right angle triangle (সমকোণী ত্রিভূজ) whose base (ভূমি) is $OR$, the radius of the base of the cylinder. Now $OP$ can never be equal to $OR$.
Problem 3:
$\triangle PAB$ and $\triangle PCD$ are similar and $\frac {\triangle PAB}{\triangle PCD} = \frac {YA}{XR}$
Problem 4:
Note that the cone has two similar triangle inside it. One is the cross section of the whole cone and another is the cross section of the part of the cone inside the cylinder. Find heights and volume of the different sections.
Try solving them now. Have I mentioned something that you don't know already?
"Go down deep enough into anything and you will find mathematics." ~Dean Schlicter
Re: BdMO(Divisional)
Why do you work so hard when you can just write it on the forum??It was made by Microsoft Paint. And I made the resolution low, coz it would have been better for me to upload it. But now I can c it was too small! And the font was by bijoy and unicode.
Anyway when you add texts to images the font quality gets worse with the quality of images reduced.
r@k€€/|/
Re: BdMO(Divisional)
@TIUrmi:
oops! the raius is half of the sphere. So the problem can be solved by Pythagoras. thnx.
oops! the raius is half of the sphere. So the problem can be solved by Pythagoras. thnx.
r@k€€/|/