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For The Mathematically Inclined

Anil Saigal
11/08/2018

Problem 1:

A lamp is used to light during Diwali hold oil up to its brim.   The diameter of the lamp is 10 cm and the height is 3 cm.  Assume the lamp is cut from a sphere at the height of 3 cm from base and ignore the thickness of the lamp. How many liters of oil does a single lamp hold?
(A picture of lamp is shown on the side)
 
Problem 2:
If the lamp in Problem 1 can burn for 12 hours, what is the height of the oil in the lamp after 6 hours.  

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Please send your solutions anil@lokvani.com. 

Use Problem Solutions M-110918 as the subject line. Please include your full name in the text of the main message. Everyone with the right answer will be acknowledged in the next issue of Lokvani. 

Please do not post your solution in Post Comments. No credit will be given for solutions not sent to anil@lokvani.com. 

If you need clarification on any problem, please contact anil@lokvani.com. 

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Problems from 10/25/18

Problem 1:
How many different flags can be made from colors purple, yellow, red, white, blue, green, orange so that each flag consisted of three different colors?

Problem 2:
In rectangle with sides 3 and 10 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?


Congratulations to Ramachandran Balakrishna who was the winner of the last set of puzzles



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