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An empty, cube-shaped swimming pool is filled part way with x cubic fe

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An empty, cube-shaped swimming pool is filled part way with x cubic fe  [#permalink]

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New post 29 Oct 2018, 21:12
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An empty, cube-shaped swimming pool is filled part way with x cubic feet of water. It is then filled the rest of the way with y cubic feet of chlorine. Which of the following, in feet, expresses the depth of the swimming pool?


A. \(x + y\)

B. \(\frac{x + y}{3}\)

C. \(\sqrt[3]{x + y}\)

D. \((x + y)^3\)

E. \(\frac{\sqrt[3]{x+y}}{3}\)

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An empty, cube-shaped swimming pool is filled part way with x cubic fe  [#permalink]

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New post Updated on: 30 Oct 2018, 00:32
An empty, cube-shaped swimming pool is filled part way with x cubic feet of water. It is then filled the rest of the way with y cubic feet of chlorine. Which of the following, in feet, expresses the depth of the swimming pool?


A. x+yx+y

B. x+y3x+y3

C. x+y‾‾‾‾‾√x+y

D. (x+y)3(x+y)3

E. x+y‾‾‾‾√33x+y33

Depth of the cube pool would be equal to the volume of the cube, given that the cube is filled first with x ft3 water and then yft3 of chlorine hence total volume would be ( x+y)^(1/3), option C

Originally posted by Archit3110 on 29 Oct 2018, 23:50.
Last edited by Archit3110 on 30 Oct 2018, 00:32, edited 1 time in total.
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Re: An empty, cube-shaped swimming pool is filled part way with x cubic fe  [#permalink]

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New post 30 Oct 2018, 00:24
Hi,

Archit3110
Why do you say "Depth of the cube pool would be equal to the volume of the cube"?

Shouldn't the depth be cube root of the volume? Considering V= S(cube) so S= V^1/3

What am I missing? Shouldn't the answer be (x+y)^1/3 ?? I can't find that in the options.

chetan2u Gladiator59 generis
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Re: An empty, cube-shaped swimming pool is filled part way with x cubic fe  [#permalink]

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New post 30 Oct 2018, 00:26
2
v= x+y
v= s^3 where s is the side.
therefore, s (height) = cube root of (x+y)
I think answer C should have cube root sign.? Bunuel
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Re: An empty, cube-shaped swimming pool is filled part way with x cubic fe  [#permalink]

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New post 30 Oct 2018, 00:30
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Re: An empty, cube-shaped swimming pool is filled part way with x cubic fe  [#permalink]

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New post 30 Oct 2018, 01:07
Cubic shaped pool volume =S^3
pool filled with x cubic feet of water. x=50
and y cubic feet of chlorine : y=14
S^3=X+Y
S(one side of cube or depth of pool)=√X+Y
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Re: An empty, cube-shaped swimming pool is filled part way with x cubic fe  [#permalink]

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New post 30 Oct 2018, 01:55
hibobotamuss wrote:
Hi,

Archit3110
Why do you say "Depth of the cube pool would be equal to the volume of the cube"?

Shouldn't the depth be cube root of the volume? Considering V= S(cube) so S= V^1/3

What am I missing? Shouldn't the answer be (x+y)^1/3 ?? I can't find that in the options.

chetan2u Gladiator59 generis


I think now the answers have been edited and C is what you are looking at..

any other query please let me know
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Re: An empty, cube-shaped swimming pool is filled part way with x cubic fe  [#permalink]

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New post 30 Oct 2018, 02:47

Solution


Given:
    • An empty, cube-shaped swimming pool is completely filled with
    o x cubic feet of water, and
    o y cubic feet of chlorine

To find:
    • Depth of the swimming pool in feet

Approach and Working:
    • Volume of water = x \(ft^3\)
    • Volume of chlorine = y \(ft^3\)

Let us assume that the depth of the pool is a ft

    • Then, the volume of the pool = \(a^3\) = volume of water + volume of chlorine
      o Implies, \(a^3 = x + y\)
      o Thus, \(a = (x + y)^{1/3}\)

Hence, the correct answer is Option C

Answer: C

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