Question 1069778: A new cylindrical tank will be installed in a pre-existing rectangular channel measuring 10 feet long, 6 feet wide, and 40 feet deep. The tank has a diameter of 42 inches and is 40 feet deep. To keep the new tank in place, soil will be dumped 20 feet high in the space between the tank and the rectangular channel.
A) How many cubic inches of space are in the cylinder? 384.65 cubic inches
B) How many cubic yards of space are in the rectangular channel before the installation or inclusion of the tank/soil? 88.88 cubic yards
C) How many cubic feet of backfill material will you need to fill the space between the tank and the rectangular channel if you were to dump the backfill material 20 feet high? 1185.76 cubic feet
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 1 cubic foot = 1728 cubic inches.
1 cubic yard = 27 cubic feet = 46656 cubic inches.
the rectangular hole is 10 feet by 6 feet by 40 feet.
the volume of the hole is therefore 10 * 6 * 40 = 2400 cubic feet.
this is equivalent to 2400 * 1728 = 4147200 cubic inches.
divide this by 46656 and you get 88.89 cubic yards.
alternatively, divide 2400 cubic feet by 27 and you get 88.89 cubic yards.
the tank has a diameter of 42 inches and is 40 feet deep.
the depth of 40 feet is equivalent to 40 * 12 = 480 inches.
the radius of the tank is 42/2 = 21 inches.
the volume of the tank is pi * 21^2 * 480 = 665012.3329 cubic inches.
divide this by 1728 and you get 384.8451001 cubic feet (not cubic inches).
if you want to fill the space between the cylinder and the hole to a depth of 20 feet, then you will need half the volume of dirt that you would need to fill the space between the cylinder and the hole to a depth of 40 feet.
the volume of the 40 foot hole in cubic feet is equal to 2400.
the volume of the 40 foot cylinder in cubic feet is equal to 384.8451001.
the difference is 2400 - 384.8451001 = 2015.1549 cubic feet.
divide that by 2 and you get 1007.57745 cubic feet of dirt to fill the space to a depth of 20 feet.
that's what i think your answer should be.
A) How many cubic inches of space are in the cylinder? 384.65 cubic inches
B) How many cubic yards of space are in the rectangular channel before the installation or inclusion of the tank/soil? 88.88 cubic yards
C) How many cubic feet of backfill material will you need to fill the space between the tank and the rectangular channel if you were to dump the backfill material 20 feet high? 1185.76 cubic feet
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