The solution would be like this for this specific problem:
Volume of a cylinder = pi * r^2 * h
Volume of a cone = 1/3 * pi * r^2 * h
Total Height = 47
Height of the cone = 12
Height of the cylinder = 35
If the top half is filled with sand, then:
volume (sand) = pi * 4^2 * 36
volume (cone) = 1/3 * pi * 4^2 * 12
Total volume = 1960.353816 cubic millimeters
353816 / (10 * pi) = 62.4 seconds.
It will take 62.4 seconds until all of the sand has dripped to the bottom of the hourglass.
Answer: 1 in 18
This is the same as writing the fraction 1/18
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Explanation:
Since she has 36 marbles total, and the probability of picking green is 1 in 2, this means (1/2)*36 = 18 marbles are green.
Then she also has (1/3)*36 = 12 red marbles and (1/9)*36 = 4 blue marbles.
So far, that accounts for 18+12+4 = 34 marbles in all. That leaves 36-4 = 2 marbles left over that must be black, as it's the only color left.
From that, the probability of choosing a black marble is 2/36 = 1/18.
There's a 1 in 18 chance of Maddy picking a black marble.
1/18 = 0.0556 = 5.56% approximately
It would take 6 minutes and 45 seconds
