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))

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Length: Width : Height = 5 : 1 : 3treker 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))

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.**

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Thanks much Anurag, but could you please explain how 3 * cube root(V/15) becomes 3/cube root(15/V)?Anurag@Gurome wrote:Length: Width : Height = 5 : 1 : 3treker 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))

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!

- Treker

- Treker

### GMAT/MBA Expert

- Anurag@Gurome
- GMAT Instructor
**Posts:**3835**Joined:**02 Apr 2010**Location:**Milpitas, CA**Thanked**: 1854 times**Followed by:**523 members**GMAT Score:**770

If you check the given options, there is no option given as 3 * cube root(V/15). And, 3 * cube root(V/15) is one and the same thing as 3/cube root(15/V). So, we chose D as the answer. See this example:treker wrote:Thanks much Anurag, but could you please explain how 3 * cube root(V/15) becomes 3/cube root(15/V)?Anurag@Gurome wrote:Length: Width : Height = 5 : 1 : 3treker 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))

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.

(2/5) Ã· 4 = (2/5) * (1/4) = 1/10

Similarly, 3 Ã· cube root(15/V) = 3 * cube root(V/15)

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