SOLUTION: Water flowed from a cylindrical tank at a constant rate of 10mL per second. The height of the tank is 1.2 metres.
a) Find the radius of the tank to the nearest cm if it takes 3 da
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Question 1118932: Water flowed from a cylindrical tank at a constant rate of 10mL per second. The height of the tank is 1.2 metres.
a) Find the radius of the tank to the nearest cm if it takes 3 days to empty the tank
b) The tank needs to be transported and is placed in a fitted rectangular box. Find the dimension and volume of the box required.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You must presume that the tank is absolutely full at the start of the three day period. Also, you need to use the fact that one milliliter of water is equal to one cubic centimeter of water.
Let 
represent the elapsed time in seconds, then is 3 days times 24 hours/day times 60 minutes per hour times 60 seconds per minute. Step 1: Calculate (Yes, you get to do your own arithmetic throughout)
Since the water flow rate out of the tank is 10 ml/second, and it went from full to empty in seconds, the volume of the tank must be 
. Step 2: Calculate and convert from milliliters to cubic centimeters (it is one to one, so easy-peasy)
The volume of a cylinder is given by:
.
You were given the height and now know the volume, so you must solve for the radius:
Since the problem is asking you to find the radius to the nearest centimeter, it is necessary to convert the height in meters to height in centimeters. There are 100 centimeters in a meter, so the height is 120 centimeters.
Round your calculation to the nearest whole number.
The rectangular box must have a square end, the INTERNAL dimensions of which must be the diameter (two times the radius) of the cylinder, and the INTERNAL dimensions of the length must be equal to the height. The volume of the interior of the box is the area of the square end times the length.
John
My calculator said it, I believe it, that settles it
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