Question

Use the fact 1ml=1 cubic centimeter to calculate the number of the gallons in a cubic foot ,solve by dimensional analysis.

Answer 1

Cubic foot is a unit of volume hence ,

one cubic foot = length x breadth x height

= 1ft x1ft x1ft = 1 ft³

now, since 1ft = 12 inches = 2.54 x12 = 30.48 cms. [ 1 inch = 2.54 cms. ]

therefore , 1ft³  = 30.48 x 30. 48 x 30.48 = 28316. 8465 cms³

again 1 cubic centimeter = 1 ml ( as given )

hence, 28316.8465 cubic centimeter = 28316.8465 ml.

One gallon (US) = 3800 ml = 3800 cubic centimeters [ one gallon = 3.8 litres = 3800 ml ]

therefore , one cubic foot = 28316 . 8465 cm³  = ( 28316.8465 / 3800 ) = 7.45180 gallons ( US )

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