cubned ical box

treker wrote:The interiors of a cubical box are designed to hold a volume of V ml. If the length, breadth, and height are in ratio 5:1:3, in terms of V which of the following equals the height of the box in cm?
(1 ml = 1 cm^3)

A. cube root(V) B. 3/cube root(3/V) C. cube root(V/15) D. 3/cube root(15/V) E. 9/(5*cube root(15/V))

treker wrote:

Anurag@Gurome wrote:

treker wrote:The interiors of a cubical box are designed to hold a volume of V ml. If the length, breadth, and height are in ratio 5:1:3, in terms of V which of the following equals the height of the box in cm?
(1 ml = 1 cm^3)

A. cube root(V) B. 3/cube root(3/V) C. cube root(V/15) D. 3/cube root(15/V) E. 9/(5*cube root(15/V))

Length: Width : Height = 5 : 1 : 3
Let us assume that Length = 5x, Width = x, and Height = 3x
Then, V = (5x)(x)(3x) implies V = 15(x^3)
x^3 = V/15 or x = cube root(V/15)
Hence, height = 3 * x = 3 * cube root(V/15) = 3/cube root(15/V)

The correct answer is D.

Thanks much Anurag, but could you please explain how 3 * cube root(V/15) becomes 3/cube root(15/V)?