Math CentralQuandaries & Queries


Question from Simon, a student:

A cylindrical tank with height 15m and diameter 2m is being filled with gasoline at a rate of 500L/min. At what rate is the fluid level in the tank rising?(1L = 1000cm^3). About how long will it take to fill the tank?


Since 1 L = 1000 cm3, 500 L/min = 500 000 cm3/min. There are 100 cm in a metre so

500 000 cm3/min = 500 000 × 1/(100)3 cm3/min × m3/cm3 = 0.5 m3/min

The volume of a cylinder is π r2 h where r is the radius and h is the height. Let f be the number of meters the fluid level rises in 1 minute then

π 12 f = 0.5

What is f?


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