Solution to Last Week's Puzzler
Architecture Puzzler #221
Suppose you have a 48-foot- (14.63-meter-) square section of concrete with a one-percent slope down to a center drain. If this center drain became plugged, how much water would the area contain before it flooded?
About 1380 gallons (5220 liters) of water. To calculate, you need to know that the volume of a pyramid is the area of the base multiplied by 1/3 its altitude. In this case the pyramid is upside-down with the drain at its apex.
Base is 48 by 48 feet = 2304 square feet
Altitude (slope X distance from edge to drain) = 0.01 X 24 feet = 0.24 feet
Volume = 2304 square feet X 1/3 X 0.24 feet = 184.32 cubic feet
At 7.48 gallons per cubic foot = 1380 gallons
Base is 14.63 by 14.63 meters = 214 square meters
Altitude (slope X distance from edge to drain) = 0.01 X 7.315 meters = 0.07315 meters
Volume = 214 square meters X 1/3 X 0.07315 meters = 5.22 cubic meters
At 1000 liters per cubic meter = 5220 liters