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| Math Central | Quandaries & Queries |
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Question from susanna, a teacher: This water tank is a perfect sphere with an inner radius of 12 metres. However, they used inferior materials to build the water tank, and the tank can only withstand a water pressure of 185 kiloPascals. Assume the density of water is exactly 1000 kg/m3, gravity is 9.8 metres/s2, and disregard atmospheric pressure. How many cubic metres of water can safely be stored in the tank? Round DOWN to the nearest whole number (since rounding up could be catastrophic in this instance!), and please submit only a number with no other information. |
Susanna,
This does not sound like a real-world problem; and RD does not "submit numbers with no other information."
Now, what you need to do:
- Where in the tank will the pressure be highest?
- How deep may the water be above that point? (A kilopascal is a kilonewton per square meter; how many newtons per square meter can the tank take? Gravity is 9.8 newtons per kilogram; how many kilograms of water may be above one square meter and how tall a column is this?)
- Look up the formula for the volume of a spherical cap (any good book of tables or go online) or use calculus to find the volume.
Good Hunting!
RD
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