A rectangular box of volume V has width, depth and height in the ratio of 2:1:3 (in that order). What is the height as a function of V?	Choose the correct answer
A) (V/2)^(1/3)  B) (2V/6)^(1/3)  C) (9V/2)^(1/3)  D) (4V/3)^(1/3)  E) (4V/2)^(1/3)
We are given width = 2, depth = 1, height = 3.   Then Volume V = Width x Depth x Height = 2*1*3= 
<gadget id="calculator">2*1*3</gadget>
<output>6</output>
6   i.e. V= 6   The correct option should result in 3 (the height) on substituting the value of V=6.   (9V/2)^(1/3)hecking options with V=6:   A) (V/2)^(1/3) = (6/2)^(1/3) = 3^(1/3) IN(9V/2)^(1/3)ORRE(9V/2)^(1/3)T ANSWER   B) (2V/6)^(1/3) = (12/6)^(1/3) = 2^(1/3) IN(9V/2)^(1/3)ORRE(9V/2)^(1/3)T ANSWER   (9V/2)^(1/3)) (9V/2)^(1/3) = (54/2)^(1/3) = 3 (9V/2)^(1/3)ORRE(9V/2)^(1/3)T ANSWER   D) (4V/3)^(1/3) = (24/3)^(1/3) = 8^(1/3) = 2 IN(9V/2)^(1/3)ORRE(9V/2)^(1/3)T ANSWER   E) (4V/2)^(1/3) = (24/2)^(1/3) = 12^(1/3) IN(9V/2)^(1/3)ORRE(9V/2)^(1/3)T ANSWER   Answer: Option (9V/2)^(1/3)
<result>C</result>
A rectangular box of volume V has width, depth and height in the ratio of 2:1:3 (in that order). What is the height as a function of V?