SOLUTION: When 10 cubic feet of water is poured into an empyt fish tank (rectangular Prism), the tank becomes 3/4 full. If the tank is 2 feet 8 inces wide and 40 inches long, how tall is the

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: When 10 cubic feet of water is poured into an empyt fish tank (rectangular Prism), the tank becomes 3/4 full. If the tank is 2 feet 8 inces wide and 40 inches long, how tall is the      Log On

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Question 260349: When 10 cubic feet of water is poured into an empyt fish tank (rectangular Prism), the tank becomes 3/4 full. If the tank is 2 feet 8 inces wide and 40 inches long, how tall is the tank?
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
First we make sure all units are the same -> 2 ft 8 in means 32 inches.
Volume of tank = LWH = 32*40 *H = 1280H
We need a proportion now:
(i) 10%2F%28%283%2F4%29%2A%281280h%29%29+=+X%2F%281280h%29
cross multiply to get
(ii) 12800H+=+960HX
divide to get
X = 13.333 cu. ft.
--
13.3333 cu ft. (12 in / ft)^3 = 1280H cu. in.
which means
17040 cu. in. = 1280H cu. in.
H = 13.3125 in.