A rectangular box of volume Y has width, depth and height in the ratio of 3:2:4 (in that order). What is the height as a function of Y?  Options
A) (4Y/6)^(1/2) B) (Y/6)^(1/2) C) (Y/4)^(1/2) D) (2Y/3)^(1/2) E) (Y)^(1/2)
We are given width = 3, depth = 2, height = 4.   Then Volume = Width x Depth x Height = 3*2*4= 
<gadget id="calculator">3*2*4</gadget>
<output>24</output>
24   i.e. Y= 24   The correct option should result in 4 (the height) on substituting the value of Y=24.   Checking options with Y=24:   (4Y/6)^(1/2)) (4Y/6)^(1/2) = (96/6)^(1/2) = 4 CORRECT (4Y/6)^(1/2)NSWER   B) (Y/6)^(1/2) = (24/6)^(1/2) = 2 INCORRECT (4Y/6)^(1/2)NSWER   C) (6Y/4)^(1/2) = (144/4)^(1/2) = 6 INCORRECT (4Y/6)^(1/2)NSWER   D) (Y/3)^(1/2) = (24/3)^(1/2) = 8^(1/2) INCORRECT (4Y/6)^(1/2)NSWER   E) (Y)^(1/2) = (24)^(1/2) INCORRECT (4Y/6)^(1/2)NSWER   (4Y/6)^(1/2)nswer: Option (4Y/6)^(1/2)
<result>A</result>
A rectangular box of volume Y has width, depth and height in the ratio of 3:2:4 (in that order). What is the height as a function of Y?